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Journal articles on the topic 'Nonautonomou'

Author: Grafiati

Published: 10 March 2023

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1

Birara Aychiluhm, Setognal, Kusse Urmale Mare, Mequannent Sharew Melaku, and Abay Woday Tadesse. "Spatial Distribution and Determinants of Nonautonomy on Decision Regarding Contraceptive Utilization among Married Reproductive-Age Women in Ethiopia: Spatial and Bayesian Multilevel Analysis." Nursing Research and Practice 2021 (November 5, 2021): 1–10. http://dx.doi.org/10.1155/2021/2160922.

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Background. Studies conducted to date in Ethiopia did not explore the spatial distribution, individual-level, and community-level factors affecting women’s nonautonomy on decision to use contraceptives. Hence, this study aimed to assess the spatial distribution of women’s nonautonomy on decision regarding contraceptive utilization and its determinants in Ethiopia. Methods. Data were accessed from the Demographic Health Survey program official database website (https://dhsprogram.com). A weighted sample of 3,668 married reproductive-age women currently using contraceptives was included in this analysis. Bayesian multilevel logistic regression models were fitted to identify the determinants of women’s nonautonomy on contraceptive utilization. Adjusted odds ratio with 95% credible interval was used to select variables that have a significant effect on nonautonomy on contraceptive utilization. Results. A high proportion of women with nonautonomy on decision regarding contraceptive utilization was found in northern parts of Southern Nations, Nationalities, and People’s Region, Southern parts of Oromia, and Benishangul-Gumuz regions of the country. Overall, 2876 (78.40% (95% CI: 77.0%, 79.7%)) women were nonautonomous on decision regarding contraceptive utilization. In the final model, age from 35–49 (AOR (95% CI) = 0.63 (0.54, 0.72)), living in the richer households (AOR (95% CI) = 0.12 (0.03, 0.26)), being married at 18 years or above (AOR (95% CI) = 0.33 (0.19, 0.57)), and residing in an rural areas (AOR (95% CI) = 1.34 (1.01, 1.71)) and metropolitan regions (AOR (95% CI) = 0.71(0.54, 0.91)) were associated with women’s nonautonomy on decision regarding contraceptive utilization. Conclusions. In Ethiopia, the spatial distribution of women’s nonautonomy on decision about contraceptive utilization was nonrandom. More than three-fourths of married reproductive-age women in Ethiopia are nonautonomous on decision regarding contraceptive utilization. Region, residence, current age, age at marriage, and wealth index were statistically associated with women’s nonautonomy on decision regarding contraceptive utilization.

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2

Balasuriya, Sanjeeva. "A Numerical Scheme for Computing Stable and Unstable Manifolds in Nonautonomous Flows." International Journal of Bifurcation and Chaos 26, no. 14 (December 30, 2016): 1630041. http://dx.doi.org/10.1142/s021812741630041x.

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There are many methods for computing stable and unstable manifolds in autonomous flows. When the flow is nonautonomous, however, difficulties arise since the hyperbolic trajectory to which these manifolds are anchored, and the local manifold emanation directions, are changing with time. This article utilizes recent results which approximate the time-variation of both these quantities to design a numerical algorithm which can obtain high resolution in global nonautonomous stable and unstable manifolds. In particular, good numerical approximation is possible locally near the anchor trajectory. Nonautonomous manifolds are computed for two examples: a Rossby wave situation which is highly chaotic, and a nonautonomus (time-aperiodic) Duffing oscillator model in which the manifold emanation directions are rapidly changing. The numerical method is validated and analyzed in these cases using finite-time Lyapunov exponent fields and exactly known nonautonomous manifolds.

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Ceballos-Lira, Marcos J., and Aroldo Pérez. "Global solutions and blowing-up solutions for a nonautonomous and nonlocal in space reaction-diffusion system with Dirichlet boundary conditions." Fractional Calculus and Applied Analysis 23, no. 4 (August 26, 2020): 1025–53. http://dx.doi.org/10.1515/fca-2020-0054.

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AbstractWe give sufficient conditions for global existence and finite time blow up of positive solutions for a nonautonomous weakly coupled system with distinct fractional diffusions and Dirichlet boundary conditions. Our approach is based on the intrinsic ultracontractivity property of the semigroups associated to distinct fractional diffusions and the study of blow up of a particular system of nonautonomus delay differential equations.

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4

Jones, Katherine H., Jingchun Liu, and P. N. Adler. "Molecular Analysis of EMS-Induced frizzled Mutations in Drosophila melanogaster." Genetics 142, no. 1 (January 1, 1996): 205–15. http://dx.doi.org/10.1093/genetics/142.1.205.

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The frizzled (fz) gene of Drosophila is essential for the development of normal tissue polarity in the adult cuticle of Drosophila. In fz mutants the parallel array of hairs and bristles that decorate the cuticle is disrupted. Previous studies have shown that fz encodes a membrane protein with seven putative transmembrane domains, and that it has a complex role in the development of tissue polarity, as there exist both cell-autonomous and cell nonautonomous alleles. We have now examined a larger number of alleles and found that 15 of 19 alleles display cell nonautonomy. We have examined these and other alleles by Western blot analysis and found that most fz mutations result in altered amounts of Fz protein, and many also result in a Fz protein that migrates aberrantly in SDS-PAGE. We have sequenced a subset of these alleles. Cell nonautonomous fz alleles were found to be associated with mutations that altered amino acids in all regions of the Fz protein. Notably, the four cell-autonomous mutations were all in a proline residue located in the presumptive first cytoplasmic loop of the protein. We have also cloned and sequenced the fz gene from D. virilis. Conceptual translation of the D. virilis open reading frame indicates that the Fz protein is unusually well conserved. Indeed, in the putative cytoplasmic domains the Fz proteins of the two species are identical.

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5

Balibrea-Iniesta, Francisco, Carlos Lopesino, Stephen Wiggins, and Ana M. Mancho. "Chaotic Dynamics in Nonautonomous Maps: Application to the Nonautonomous Hénon Map." International Journal of Bifurcation and Chaos 25, no. 12 (November 2015): 1550172. http://dx.doi.org/10.1142/s0218127415501722.

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In this paper, we analyze chaotic dynamics for two-dimensional nonautonomous maps through the use of a nonautonomous version of the Conley–Moser conditions given previously. With this approach we are able to give a precise definition of what is meant by a chaotic invariant set for nonautonomous maps. We extend the nonautonomous Conley–Moser conditions by deriving a new sufficient condition for the nonautonomous chaotic invariant set to be hyperbolic. We consider the specific example of a nonautonomous Hénon map and give sufficient conditions, in terms of the parameters defining the map, for the nonautonomous Hénon map to have a hyperbolic chaotic invariant set.

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6

Ferreira Alves, João, and Luís Silva. "Nonautonomous Graphs and Topological Entropy of Nonautonomous Lorenz Systems." International Journal of Bifurcation and Chaos 25, no. 06 (June 15, 2015): 1550079. http://dx.doi.org/10.1142/s0218127415500790.

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In this work, we associate a p-periodic nonautonomous graph to each p-periodic nonautonomous Lorenz system with finite critical orbits. We develop Perron–Frobenius theory for nonautonomous graphs and use it to calculate their entropy. Finally, we prove that the topological entropy of a p-periodic nonautonomous Lorenz system is equal to the entropy of its associated nonautonomous graph.

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7

Salman, Mohammad, and Ruchi Das. "Dynamics of Weakly Mixing Nonautonomous Systems." International Journal of Bifurcation and Chaos 29, no. 09 (August 2019): 1950123. http://dx.doi.org/10.1142/s0218127419501232.

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For a commutative nonautonomous dynamical system we show that topological transitivity of the nonautonomous system induced on probability measures (hyperspaces) is equivalent to the weak mixing of the induced systems. Several counter examples are given for the results which are true in autonomous but need not be true in nonautonomous systems. Wherever possible sufficient conditions are obtained for the results to hold true. For a commutative periodic nonautonomous system on intervals, it is proved that weak mixing implies Devaney chaos. Given a periodic nonautonomous system, it is shown that sensitivity is equivalent to some stronger forms of sensitivity on a closed unit interval.

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8

Li, Nan, and Lidong Wang. "Sensitivity and Chaoticity on Nonautonomous Dynamical Systems." International Journal of Bifurcation and Chaos 30, no. 10 (August 2020): 2050146. http://dx.doi.org/10.1142/s0218127420501461.

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This paper discusses the sensitivity and chaotic properties of nonautonomous dynamical systems. For the first time we obtain sufficient conditions of some stronger forms of sensitivity for nonautonomous dynamical systems. Then, some chaotic relations between two nonautonomous dynamical systems are proved.

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9

Grines, V. Z., and L. M. Lerman. "Nonautonomous dynamics: classification, invariants, and implementation." Contemporary Mathematics. Fundamental Directions 68, no. 4 (December 15, 2022): 596–620. http://dx.doi.org/10.22363/2413-3639-2022-68-4-596-620.

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The work is a brief review of the results obtained in nonautonomous dynamics based on the concept of uniform equivalence of nonautonomous systems. This approach to the study of nonautonomous systems was proposed in [10] and further developed in the works of the second author, and recently - jointly by both authors. Such an approach seems to be fruitful and promising, since it allows one to develop a nonautonomous analogue of the theory of dynamical systems for the indicated classes of systems and give a classi cation of some natural classes of nonautonomous systems using combinatorial type invariants. We show this for classes of nonautonomous gradient-like vector elds on closed manifolds of dimensions one, two, and three. In the latter case, a new equivalence invariant appears, the wild embedding type for stable and unstable manifolds [14,17], as shown in a recent paper by the authors [5].

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10

Lerman, L. M., and L. P. Shil’nikov. "Homoclinical structures in nonautonomous systems: Nonautonomous chaos." Chaos: An Interdisciplinary Journal of Nonlinear Science 2, no. 3 (July 1992): 447–54. http://dx.doi.org/10.1063/1.165887.

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11

Petrie, Bradford. "NONAUTONOMOUS PSYCHOLOGY." Southern Journal of Philosophy 28, no. 4 (December 1990): 539–59. http://dx.doi.org/10.1111/j.2041-6962.1990.tb00558.x.

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12

Soffer, A., and M. I. Weinstein. "Nonautonomous Hamiltonians." Journal of Statistical Physics 93, no. 1/2 (October 1998): 359–91. http://dx.doi.org/10.1023/b:joss.0000026738.52652.6e.

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13

KILIÇ, RECAI. "EXPERIMENTAL MODIFICATIONS OF VOA-BASED AUTONOMOUS AND NONAUTONOMOUS CHUA'S CIRCUITS FOR HIGHER DIMENSIONAL OPERATION." International Journal of Bifurcation and Chaos 16, no. 09 (September 2006): 2649–58. http://dx.doi.org/10.1142/s0218127406016318.

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In order to operate in higher dimensional form of autonomous and nonautonomous Chua's circuits keeping their original chaotic behaviors, we have experimentally modified VOA (Voltage Mode Operational Amplifier)-based autonomous Chua's circuit and nonautonomous MLC [Murali–Lakshmanan–Chua] circuit by using a simple experimental method. After introducing this experimental method, we will present PSpice simulation and experimental results of modified high dimensional autonomous and nonautonomous Chua's circuits.

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14

Doungmo Goufo, E. F., and S. C. Oukouomi Noutchie. "Global Analysis of a Discrete Nonlocal and Nonautonomous Fragmentation Dynamics Occurring in a Moving Process." Abstract and Applied Analysis 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/484391.

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We use a double approximation technique to show existence result for a nonlocal and nonautonomous fragmentation dynamics occurring in a moving process. We consider the case where sizes of clusters are discrete and fragmentation rate is time, position, and size dependent. Our system involving transport and nonautonomous fragmentation processes, where in addition, new particles are spatially randomly distributed according to some probabilistic law, is investigated by means of forward propagators associated with evolution semigroup theory and perturbation theory. The full generator is considered as a perturbation of the pure nonautonomous fragmentation operator. We can therefore make use of the truncation technique (McLaughlin et al., 1997), the resolvent approximation (Yosida, 1980), Duhamel formula (John, 1982), and Dyson-Phillips series (Phillips, 1953) to establish the existence of a solution for a discrete nonlocal and nonautonomous fragmentation process in a moving medium, hereby, bringing a contribution that may lead to the proof of uniqueness of strong solutions to this type of transport and nonautonomous fragmentation problem which remains unsolved.

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15

Salman, Mohammad, Xinxing Wu, and Ruchi Das. "Sensitivity of Nonautonomous Dynamical Systems on Uniform Spaces." International Journal of Bifurcation and Chaos 31, no. 01 (January 2021): 2150017. http://dx.doi.org/10.1142/s0218127421500176.

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We introduce the concepts of sensitivity, multisensitivity, cofinite sensitivity, and syndetic sensitivity for nonautonomous dynamical systems on uniform spaces and obtain some sufficient conditions under which topological transitivity and dense periodic points imply sensitivity for nonautonomous systems on Hausdorff uniform spaces. We also study sensitivity and other stronger versions of sensitivity for the systems induced on hyperspaces and for the product of nonautonomous dynamical systems on uniform spaces.

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16

Yu, Jiali, Wenhuo Su, and Dongmei Xu. "Backwards Asymptotically Autonomous Dynamics for 2D MHD Equations." Discrete Dynamics in Nature and Society 2018 (September 23, 2018): 1–11. http://dx.doi.org/10.1155/2018/4948301.

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We consider the backwards topological property of pullback attractors for the nonautonomous MHD equations. Under some backwards assumptions of the nonautonomous force, it is shown that the theoretical existence result for such an attractor is derived from an increasing, bounded pullback absorbing and the backwards pullback flattening property. Meanwhile, some abstract results on the convergence of nonautonomous pullback attractors in asymptotically autonomous problems are established and applied to MHD equations.

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17

ÇAM, UǦUR, and RECAİ KILIÇ. "INDUCTORLESS REALIZATION OF NONAUTONOMOUS MLC CHAOTIC CIRCUIT USING CURRENT-FEEDBACK OPERATIONAL AMPLIFIERS." Journal of Circuits, Systems and Computers 14, no. 01 (February 2005): 99–107. http://dx.doi.org/10.1142/s0218126605002180.

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An inductorless realization of nonautonomous (Murali–Lakshmanan–Chua) MLC chaotic circuit is proposed. The main purpose of this study is to improve the performance of nonautonomous MLC chaotic circuit using only CFOAs. CFOA-based topology used in this realization enables to simulate floating inductance. This modification provides to the designer wideband chaotic signals for secure communication systems. In addition to this major improvement, a CFOA-based nonlinear resistor was used in the new realization of nonautonomous MLC chaotic circuit. The usage of CFOA-based inductance simulator and nonlinear resistor in the circuit structure reduces the component count and provides isolated outputs. The performance of the proposed inductorless nonautonomous chaotic circuit is demonstrated with both PSpice simulations and experimental results.

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18

KOKSCH, NORBERT. "A CONTRIBUTION TO NONAUTONOMOUS INERTIAL MANIFOLDS." Stochastics and Dynamics 04, no. 03 (September 2004): 317–34. http://dx.doi.org/10.1142/s0219493704001097.

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19

Nakamura, Yuki. "Evil as a social action." Thesis Eleven 144, no. 1 (February 2018): 46–58. http://dx.doi.org/10.1177/0725513618756090.

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This paper explores how to theoretically transcend the division that exists between nonautonomous and autonomous evil. Evil in the context of this paper is a social action that harms others against their will. Traditional social theory has explained the evil in modernity as a pathology or as the result of the organizational and bureaucratic structures of society that was beyond the agency of individuals. The concepts of nonautonomous and autonomous evil developed by John Kekes are used to clarify the types of evil as a social action. It follows that structural processes that entail agency can also be applied to unify the different approaches given to evil and fill the misleading gap that exists between nonautonomous and autonomous evil. Regardless of the event or the perpetrator, evil is agency-driven and is always composed of both nonautonomous and autonomous evil. What differs is the degree of nonautonomous or autonomous evil in the social action. It shows that evil is an important part of agency regardless of the agent’s awareness of the evil that actions entail within modernity, and it is therefore the task of social theory to shed light on its social processes.

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20

CONG, NGUYEN DINH. "LYAPUNOV SPECTRUM OF NONAUTONOMOUS LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS." Stochastics and Dynamics 01, no. 01 (March 2001): 127–57. http://dx.doi.org/10.1142/s0219493701000084.

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We introduce a concept of Lyapunov exponents and Lyapunov spectrum for nonautonomous linear stochastic differential equations. The Lyapunov exponents are defined samplewise via the two-parameter flow generated by the equation. We prove that Lyapunov exponents are finite and nonrandom. Lyapunov exponents are used for investigation of Lyapunov regularity and stability of nonautonomous stochastic differential equations. The results show that the concept of Lyapunov exponents is still very fruitful for stochastic objects and gives us a useful tool for investigating sample stability as well as qualitative behavior of nonautonomous linear and nonlinear stochastic differential equations.

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21

Wu, Delin. "The Pullback Attractors for the Nonautonomous Camassa-Holm Equations." Mathematical Problems in Engineering 2009 (2009): 1–12. http://dx.doi.org/10.1155/2009/390805.

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We consider the pullback attractors for the three-dimensional nonautonomous Camassa-Holm equations in the periodic box . Assuming , which is translation bounded, the existence of the pullback attractor for the three-dimensional nonautonomous Camassa-Holm system is proved in and .

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22

Anguiano, María. "Attractors for a Nonautonomous Liénard Equation." International Journal of Bifurcation and Chaos 25, no. 02 (February 2015): 1550032. http://dx.doi.org/10.1142/s0218127415500327.

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In this paper, we prove the existence of pullback and uniform attractors for a nonautonomous Liénard equation. The relation among these attractors is also discussed. After that, we consider that the Liénard equation includes forcing terms which belong to a class of functions extending periodic and almost periodic functions recently introduced by Kloeden and Rodrigues [2011]. Finally, we estimate the Hausdorff dimension of the pullback attractor. We illustrate these results with a numerical simulation: we present a simulation showing the pullback attractor for the nonautonomous Van der Pol equation, an important special case of the nonautonomous Liénard equation.

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23

KLOEDEN, P. E., and S. SIEGMUND. "BIFURCATIONS AND CONTINUOUS TRANSITIONS OF ATTRACTORS IN AUTONOMOUS AND NONAUTONOMOUS SYSTEMS." International Journal of Bifurcation and Chaos 15, no. 03 (March 2005): 743–62. http://dx.doi.org/10.1142/s0218127405012454.

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Nonautonomous bifurcation theory studies the change of attractors of nonautonomous systems which are introduced here with the process formalism as well as the skew product formalism.We present a total stability theorem ensuring the existence of nearby attractors of perturbed systems. They depend continuously on a parameter if and only if the attraction is uniform w.r.t. parameter, i.e. the attractors are equiattracting.We apply these principles to explicit systems to clarify the meaning of continuous and abrupt transitions of attractors in contrast to bifurcations, i.e. splitting of minimal invariant subsets into others within the attractor. Several examples are treated, including a nonautonomous pitchfork bifurcation.

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24

van der Mee, Cornelis. "Nonautonomous Exponential Dichotomy." Integral Equations and Operator Theory 59, no. 4 (October 18, 2007): 591–96. http://dx.doi.org/10.1007/s00020-007-1535-8.

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25

Wang, Liang, Bochen Wang, Jiahui Peng, Xiaole Yue, and Wei Xu. "Stochastic Response of a Vibro-Impact System via a New Impact-to-Impact Mapping." International Journal of Bifurcation and Chaos 31, no. 08 (June 26, 2021): 2150139. http://dx.doi.org/10.1142/s021812742150139x.

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In this paper, a new impact-to-impact mapping is constructed to investigate the stochastic response of a nonautonomous vibro-impact system. The significant feature lies in the choice of Poincaré section, which consists of impact surface and codimensional time. Firstly, we construct a new impact-to-impact mapping to calculate the one-step transition probability matrix from a given impact to the next. Then, according to the matrix, we can investigate the stochastic responses of a nonautonomous vibro-impact system at the impact instants. The new impact-to-impact mapping is smooth and it effectively overcomes the nondifferentiability caused by the impact. A linear and a nonlinear nonautonomous vibro-impact systems are analyzed to verify the effectiveness of the strategy. The stochastic P-bifurcations induced by the noise intensity and system parameters are studied at the impact instants. Compared with Monte Carlo simulations, the new impact-to-impact strategy is accurate for nonautonomous vibro-impact systems with arbitrary restitution coefficients.

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26

Sutrima, Sutrima, Christiana Rini Indrati, and Lina Aryati. "Controllability and Observability of Nonautonomous Riesz-Spectral Systems." Abstract and Applied Analysis 2018 (2018): 1–10. http://dx.doi.org/10.1155/2018/4210135.

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There are many industrial and biological reaction diffusion systems which involve the time-varying features where certain parameters of the system change during the process. A part of the transport-reaction phenomena is often modelled as an abstract nonautonomous equation generated by a (generalized) Riesz-spectral operator on a Hilbert space. The basic problems related to the equations are existence of solutions of the equations and how to control dynamical behaviour of the equations. In contrast to the autonomous control problems, theory of controllability and observability for the nonautonomous systems is less well established. In this paper, we consider some relevant aspects regarding the controllability and observability for the nonautonomous Riesz-spectral systems including the Sturm-Liouville systems using a C0-quasi-semigroup approach. Three examples are provided. The first is related to sufficient conditions for the existence of solutions and the others are to confirm the approximate controllability and observability of the nonautonomous Riesz-spectral systems and Sturm-Liouville systems, respectively.

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27

Yang, Xin-Guang, and Jun-Tao Li. "Upper Semicontinuous Property of Uniform Attractors for the 2D Nonautonomous Navier-Stokes Equations with Damping." Abstract and Applied Analysis 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/861292.

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Our aim is to investigate the long-time behavior in terms of upper semicontinuous property of uniform attractors for the 2D nonautonomous Navier-Stokes equations with linear damping and nonautonomous perturbation external force, that is, the convergence of corresponding attractors when the perturbation tends to zero.

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Villa-Morales, José. "Hyers-Ulam stability of a nonautonomous semilinear equation with fractional diffusion." Demonstratio Mathematica 53, no. 1 (October 21, 2020): 269–76. http://dx.doi.org/10.1515/dema-2020-0021.

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AbstractIn this paper, we study the Hyers-Ulam stability of a nonautonomous semilinear reaction-diffusion equation. More precisely, we consider a nonautonomous parabolic equation with a diffusion given by the fractional Laplacian. We see that such a stability is a consequence of a Gronwall-type inequality.

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Serkin, V. N., Akira Hasegawa, and T. L. Belyaeva. "Solitary waves in nonautonomous nonlinear and dispersive systems: nonautonomous solitons." Journal of Modern Optics 57, no. 14-15 (March 2010): 1456–72. http://dx.doi.org/10.1080/09500341003624750.

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30

Pötzsche, Christian, and Evamaria Russ. "Reduction principle at work." Nonautonomous Dynamical Systems 8, no. 1 (January 1, 2021): 46–74. http://dx.doi.org/10.1515/msds-2020-0124.

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Abstract The purpose of this informal paper is three-fold: First, filling a gap in the literature, we provide a (necessary and sufficient) principle of linearized stability for nonautonomous difference equations in Banach spaces based on the dichotomy spectrum. Second, complementing the above, we survey and exemplify an ambient nonautonomous and infinite-dimensional center manifold reduction, that is Pliss’s reduction principle suitable for critical stability situations. Third, these results are applied to integrodifference equations of Hammerstein- and Urysohn-type both in C- and Lp -spaces. Specific features of the nonautonomous case are underlined. Yet, for the simpler situation of periodic time-dependence even explicit computations are feasible.

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COLONIUS, FRITZ, PETER E. KLOEDEN, and MARTIN RASMUSSEN. "MORSE SPECTRUM FOR NONAUTONOMOUS DIFFERENTIAL EQUATIONS." Stochastics and Dynamics 08, no. 03 (September 2008): 351–63. http://dx.doi.org/10.1142/s0219493708002342.

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The concept of a Morse decomposition consisting of nonautonomous sets is reviewed for linear cocycle mappings w.r.t. the past, future and all-time convergences. In each case, the set of accumulation points of the finite-time Lyapunov exponents corresponding to points in a nonautonomous set is shown to be an interval. For a finest Morse decomposition, the Morse spectrum is defined as the union of all of the above accumulation point intervals over the different nonautonomous sets in such a finest Morse decomposition. In addition, Morse spectrum is shown to be independent of which finest Morse decomposition is used, when more than one exists.

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Luo, Huming, and Zhenshan Lin. "A Dynamic Inversion Model of the Beijing Local Climate." Weather and Forecasting 29, no. 3 (June 1, 2014): 614–22. http://dx.doi.org/10.1175/waf-d-13-00011.1.

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Abstract A nonautonomous dynamic inverse model based on the autonomous dynamic inverse model is presented in this paper. By introducing the extrinsic cycle driving force and the surrounding environment driving force, the Beijing local climatic model is established via the nonautonomous dynamic inverse method. The model not only has a certain ability to predict but can relatively accurately reveal the inherent dynamic mechanisms among the monthly average atmospheric pressure, temperature, and precipitation. The model also applies to describing the dynamic characteristics of the departure from the annual cycle. The nonautonomous inversion dynamic model has broad application potential, which provides a new method for understanding and predicting local climate.

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Megan, Mihail, Traian Ceauşu, and Mihaela Aurelia Tomescu. "On Polynomial Stability of Variational Nonautonomous Difference Equations in Banach Spaces." International Journal of Analysis 2013 (March 27, 2013): 1–7. http://dx.doi.org/10.1155/2013/407958.

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Our goal in this paper is to give characterizations for some concepts of polynomial stability for variational nonautonomous difference equations. The obtained results can be considered generalizations for the case of variational nonautonomous difference equations of some theorems proved by Barbashin (1967), Datko (1973), and Lyapunov (1992), for evolution operators.

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Huo, Hai-Feng, and Wan-Tong Li. "Dynamics of a nonautonomous semiratio-dependent predator-prey system with nonmonotonic functional responses." Discrete Dynamics in Nature and Society 2006 (2006): 1–19. http://dx.doi.org/10.1155/ddns/2006/70656.

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A nonautonomous semiratio-dependent predator-prey system with nonmonotonic functional responses is investigated. For general nonautonomous case, positive invariance, permanence, and globally asymptotic stability for the system are studied. For the periodic (almost periodic) case, sufficient conditions for existence, uniqueness, and stability of a positive periodic (almost periodic) solution are obtained.

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CHEN, YUN, and XIAOFENG WU. "GLOBAL CHAOS SYNCHRONIZATION OF NONAUTONOMOUS GYROSTAT SYSTEMS VIA VARIABLE SUBSTITUTION CONTROL." International Journal of Bifurcation and Chaos 18, no. 12 (December 2008): 3719–30. http://dx.doi.org/10.1142/s0218127408022676.

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This paper suggests a master-slave nonautonomous synchronization scheme with variable substitution control. According to the scheme, some sufficient algebraic criteria for global chaos synchronization of the master and slave nonautonomous gyrostat systems via various single-variable coupling are derived. The effectiveness of the obtained criteria is numerically verified by some examples.

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TRAORÉ, BAKARY, OUSMANE KOUTOU, and BOUREIMA SANGARÉ. "GLOBAL DYNAMICS OF A SEASONAL MATHEMATICAL MODEL OF SCHISTOSOMIASIS TRANSMISSION WITH GENERAL INCIDENCE FUNCTION." Journal of Biological Systems 27, no. 01 (March 2019): 19–49. http://dx.doi.org/10.1142/s0218339019500025.

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In this paper, we investigate a nonautonomous and an autonomous model of schistosomiasis transmission with a general incidence function. Firstly, we formulate the nonautonomous model by taking into account the effect of climate change on the transmission. Through rigorous analysis via theories and methods of dynamical systems, we show that the nonautonomous model has a globally asymptotically stable disease-free periodic equilibrium when the associated basic reproduction ratio [Formula: see text] is less than unity. Otherwise, the system admits at least one positive periodic solutions if [Formula: see text] is greater than unity. Secondly, using the average of periodic functions, we further derive the autonomous model associated with the nonautonomous model. Therefore, we show that the disease-free equilibrium of the autonomous model is locally and globally asymptotically stable when the associated reproduction ratio [Formula: see text] is less than unity. When [Formula: see text] is greater than unity, the existence and global asymptotic stability of the endemic equilibrium is established under certain conditions. Finally, using linear and nonlinear specific incidence function, we perform some numerical simulations to illustrate our theoretical results.

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37

CARABALLO, TOMÁS, JOSÉ A. LANGA, FELIPE RIVERO, and ALEXANDRE N. CARVALHO. "A GRADIENT-LIKE NONAUTONOMOUS EVOLUTION PROCESS." International Journal of Bifurcation and Chaos 20, no. 09 (September 2010): 2751–60. http://dx.doi.org/10.1142/s0218127410027337.

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In this paper we consider a dissipative damped wave equation with nonautonomous damping of the form [Formula: see text] in a bounded smooth domain Ω ⊂ ℝn with Dirichlet boundary conditions, where f is a dissipative smooth nonlinearity and the damping β : ℝ → (0, ∞) is a suitable function. We prove, if (1) has finitely many equilibria, that all global bounded solutions of (1) are backwards and forwards asymptotic to equilibria. Thus, we give a class of examples of nonautonomous evolution processes for which the structure of the pullback attractors is well understood. That complements the results of [Carvalho & Langa, 2009] on characterization of attractors, where it was shown that a small nonautonomous perturbation of an autonomous gradient-like evolution process is also gradient-like. Note that the evolution process associated to (1) is not a small nonautonomous perturbation of any autonomous gradient-like evolution processes. Moreover, we are also able to prove that the pullback attractor for (1) is also a forwards attractor and that the rate of attraction is exponential.

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38

Lan, Yaoyao. "Sensitivity of Fuzzy Nonautonomous Dynamical Systems." European Journal of Pure and Applied Mathematics 12, no. 4 (October 31, 2019): 1689–700. http://dx.doi.org/10.29020/nybg.ejpam.v12i4.3573.

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This paper is devoted to a study of relations between two forms of sensitivity of nonautonomous dynamical system and its induced fuzzy systems. More specially, we study strong sensitivity and mean sensitivity in an original nonautonomous system and its connections with the same ones in its induced system, including set-valued system and fuzzified system.

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39

Zhang, Bin, and Lei Liu. "A Billingsley type theorem for Bowen topological entropy of nonautonomous dynamical systems." Open Mathematics 20, no. 1 (January 1, 2022): 1715–22. http://dx.doi.org/10.1515/math-2022-0541.

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Abstract This article is devoted to the study of the Bowen topological entropy for nonautonomous dynamical systems, which is an extension of the classical definition of Bowen topological entropy. We show that the Bowen topological entropy can be determined by the local entropies of measures for nonautonomous dynamical systems, which extends Ma and Wen’s result.

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40

Sutrima, Sutrima, Christiana Rini Indrati, and Lina Aryati. "Exact Null Controllability, Stabilizability, and Detectability of Linear Nonautonomous Control Systems: A Quasisemigroup Approach." Abstract and Applied Analysis 2018 (November 1, 2018): 1–12. http://dx.doi.org/10.1155/2018/3791609.

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In the theory control systems, there are many various qualitative control problems that can be considered. In our previous work, we have analyzed the approximate controllability and observability of the nonautonomous Riesz-spectral systems including the nonautonomous Sturm-Liouville systems. As a continuation of the work, we are concerned with the analysis of stability, stabilizability, detectability, exact null controllability, and complete stabilizability of linear non-autonomous control systems in Banach spaces. The used analysis is a quasisemigroup approach. In this paper, the stability is identified by uniform exponential stability of the associated C0-quasisemigroup. The results show that, in the linear nonautonomous control systems, there are equivalences among internal stability, stabizability, detectability, and input-output stability. Moreover, in the systems, exact null controllability implies complete stabilizability.

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41

WANG, BIXIANG. "UNIFORM ATTRACTORS OF NONAUTONOMOUS DISCRETE REACTION–DIFFUSION SYSTEMS IN WEIGHTED SPACES." International Journal of Bifurcation and Chaos 18, no. 03 (March 2008): 695–716. http://dx.doi.org/10.1142/s0218127408020598.

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We study the asymptotic behavior of nonautonomous discrete Reaction–Diffusion systems defined on multidimensional infinite lattices. We show that the nonautonomous systems possess uniform attractors which attract all solutions uniformly with respect to the translations of external terms when time goes to infinity. These attractors are compact subsets of weighted spaces, and contain all bounded solutions of the system. The upper semicontinuity of the uniform attractors is established when an infinite-dimensional reaction–diffusion system is approached by a family of finite-dimensional systems. We also examine the limiting behavior of lattice systems with almost periodic, rapidly oscillating external terms in weighted spaces. In this case, it is proved that the uniform global attractors of nonautonomous systems converge to the global attractor of an averaged autonomous system.

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42

Aulbach, Bernd, and Nguyen Van Minh. "Bounded and almost periodic solutions and evolution semigroups associated with nonautonomous functional differential equations." Abstract and Applied Analysis 5, no. 4 (2000): 245–63. http://dx.doi.org/10.1155/s1085337501000367.

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We study evolution semigroups associated with nonautonomous functional differential equations. In fact, we convert a given functional differential equation to an abstract autonomous evolution equation and then derive a representation theorem for the solutions of the underlying functional differential equation. The representation theorem is then used to study the boundedness and almost periodicity of solutions of a class of nonautonomous functional differential equations.

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43

Nickel, Gregor. "Evolution semigroups for nonautonomous Cauchy problems." Abstract and Applied Analysis 2, no. 1-2 (1997): 73–95. http://dx.doi.org/10.1155/s1085337597000286.

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In this paper, we characterize wellposedness of nonautonomous, linear Cauchy problems(NCP) {u˙(t)=A(t)u(t)u(s)=x∈Xon a Banach spaceXby the existence of certain evolution semigroups.Then, we use these generation results for evolution semigroups to derive wellposedness for nonautonomous Cauchy problems under some “concrete” conditions. As a typical example, we discuss the so called “parabolic” case.

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44

Su, Chuan-Qi, Yi-Tian Gao, Qi-Min Wang, Jin-Wei Yang, and Da-Wei Zuo. "Nonautonomous solitons in terms of the double Wronskian determinant for a variable-coefficient Gross–Pitaevskii equation in the Bose–Einstein condensate." Modern Physics Letters B 30, no. 09 (April 10, 2016): 1650103. http://dx.doi.org/10.1142/s0217984916501037.

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Under investigation in this paper is a variable-coefficient Gross–Pitaevskii equation which describes the Bose–Einstein condensate. Lax pair, bilinear forms and bilinear Bäcklund transformation for the equation under some integrable conditions are derived. Based on the Lax pair and bilinear forms, double Wronskian solutions are constructed and verified. The [Formula: see text]th-order nonautonomous solitons in terms of the double Wronskian determinant are given. Propagation and interaction for the first- and second-order nonautonomous solitons are discussed from three cases. Amplitudes of the first- and second-order nonautonomous solitons are affected by a real parameter related to the variable coefficients, but independent of the gain-or-loss coefficient [Formula: see text] and linear external potential coefficient [Formula: see text]. For Case 1 [Formula: see text], [Formula: see text] leads to the accelerated propagation of nonautonomous solitons. Parabolic-, cubic-, exponential- and cosine-type nonautonomous solitons are exhibited due to the different choices of [Formula: see text]. For Case 2 [Formula: see text], if the real part of the spectral parameter equals 0, stationary soliton can be formed. If we take the harmonic external potential coefficient [Formula: see text] as a positive constant and let the real parts of the two spectral parameters be the same, bound-state-like structures can be formed, but there are only one attractive and two repulsive procedures. For Case 3 [[Formula: see text] and [Formula: see text] are taken as nonzero constants], head-on interaction, overtaking interaction and bound-state structure can be formed based on the signs of the two spectral parameters.

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45

Li, Yangrong, and Hongyong Cui. "Pullback Attractor for Nonautonomous Ginzburg-Landau Equation with Additive Noise." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/921750.

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Long time behavior of stochastic Ginzburg-Landau equations with nonautonomous deterministic external forces, dispersion coefficients, and nonautonomous perturbations is studied. The domain is taken as a bounded intervalIinR. By making use of Sobolev embeddings and Gialiardo-Nirenberg inequality we obtain the existence and upper semicontinuity of the pullback attractor inL2(I)for the equation. The upper semicontinuity shows the stability of attractors under perturbations.

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46

Ding, Xiaohua. "Exponential stability of a kind of stochastic delay difference equations." Discrete Dynamics in Nature and Society 2006 (2006): 1–9. http://dx.doi.org/10.1155/ddns/2006/94656.

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We present a Razumilchin-type theorem for stochastic delay difference equation, and use it to investigate the mean square exponential stability of a kind of nonautonomous stochastic difference equation which may also be viewed as an approximation of a nonautonomous stochastic delay integrodifferential equations (SDIDEs), and of a difference equation arises from some of the earliest mathematical models of the macroeconomic trade cycle with the environmental noise.

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47

Do, Trong Tan, Duc Chuyen Tran, Duy Tung Le, and Phuong Nam Dao. "A Direct Reinforcement Learning Approach for Nonautonomous Thermoacoustic Generator." Mathematical Problems in Engineering 2022 (May 31, 2022): 1–11. http://dx.doi.org/10.1155/2022/6512906.

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For nonautonomous nonlinear systems, the optimal control design is affected by the terms of partial derivative. If a reinforcement learning (RL) strategy is developed to approximate the optimal control scheme in nonautonomous nonlinear systems, then the closed control system might be unstabilizing. Therefore, in this article, the approach of direct RL law for a nonautonomous thermoacoustic generator (TAG) is investigated. We establish the mathematical model of TAG by partial differential equations (PDEs) and then transforming them into time varying nonlinear systems. The direct RL technique with Newton–Leibniz formula is implemented to consider the partial derivative term from classical policy iteration (PI) method by modifying the computation using data collection between the two sampling times. Finally, several simulation studies with some comparisons are conducted to validate the theoretical analyses.

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Zhang, Junhua, Wei Zhang, and Yuxin Hao. "Multipulse Chaotic Dynamics for Nonautonomous Nonlinear Systems and Application to a FGM Plate." International Journal of Bifurcation and Chaos 24, no. 05 (May 2014): 1450068. http://dx.doi.org/10.1142/s0218127414500680.

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The extended Melnikov method is improved to investigate the nonautonomous nonlinear dynamical system in Cartesian coordinate. The multipulse chaotic dynamics of a simply supported functionally graded materials (FGM) rectangular plate subjected to transversal and in-plane excitations is investigated in this paper for the first time. The formulas of the FGM rectangular plate are two-degree-of-freedom nonautonomous nonlinear system with coupling of nonlinear terms including several square and cubic terms. The extended Melnikov method is improved to enable us to analyze directly the nonautonomous nonlinear dynamical system of the simply-supported FGM rectangular plate. The results obtained here indicate that multipulse chaotic motions can occur in the simply-supported FGM rectangular plate. Numerical simulation is also employed to find the multipulse chaotic motions of the simply-supported FGM rectangular plate.

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Chen, Xuefei, Bingyue Liu, and Huizhao Liu. "Exponential synchronization and anti-synchronization of nonautonomous chaotic systems with uncertain parameters via adaptive control." International Journal of Modern Physics C 31, no. 10 (August 3, 2020): 2050137. http://dx.doi.org/10.1142/s0129183120501375.

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The exponential synchronization and anti-synchronization of nonautonomous chaotic systems with uncertain parameters are studied. The adaptive controller is designed and analytic expression of the controller and the adaptive laws of parameters are given. Based on the Lyapunov stability theory, the exponential stability of the error system is proved. Numerical simulations of two nonautonomous chaotic systems with uncertain parameters are presented to illustrate the ability and effectiveness of the proposed method.

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50

Pourbarat, Mehdi. "On some kinds of dense orbits in general nonautonomous dynamical systems." Nonautonomous Dynamical Systems 7, no. 1 (November 4, 2020): 163–75. http://dx.doi.org/10.1515/msds-2020-0116.

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AbstractWe study the theory of universality for the nonautonomous dynamical systems from topological point of view related to hypercyclicity. The conditions are provided in a way that Birkhoff transitivity theorem can be extended. In the context of generalized linear nonautonomous systems, we show that either one of the topological transitivity or hypercyclicity give sensitive dependence on initial conditions. Meanwhile, some examples are presented for topological transitivity, hypercyclicity and topological conjugacy.

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