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Статті в журналах з теми "Stabilité des equilibres"

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Автор: Grafiati

Опубліковано: 7 липня 2024

Оновлено: 7 липня 2024

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1

Tan, Kok-Keong, Jian Yu, and Xian-Zhi Yuan. "Stability of production economies." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 61, no. 2 (October 1996): 162–70. http://dx.doi.org/10.1017/s1446788700000173.

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AbstractIn this paper, the concept of essential equilibria for production economies is first given. We then prove that in ‘most’ production economies (in the sense of Baire category) all equilibria are essential.

2

Shnol, Emmanuil. "Stability of equilibria." Scholarpedia 2, no. 3 (2007): 2770. http://dx.doi.org/10.4249/scholarpedia.2770.

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3

Evans, George W., and Bruce McGough. "REPRESENTATIONS AND SUNSPOT STABILITY." Macroeconomic Dynamics 15, no. 1 (February 22, 2010): 80–92. http://dx.doi.org/10.1017/s1365100509991015.

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By endowing his agents with simple forecasting models, or representations, M. Woodford (“Learning to Believe in Sunspots,” Econometrica 58, 277–307, 1990) found that finite state Markov sunspot equilibria may be stable under learning. We show that common factor representations generalize to all sunspot equilibria the representations used by Woodford. We find that if finite state Markov sunspots are stable under learning then all sunspots are stable under learning, provided common factor representations are used.

4

Kozlov, V. V. "Neanaliticheskie pervye integraly analiticheskikh sistem differentsial'nykh uravneniy v okrestnosti ustoychivykh polozheniy ravnovesiya." Дифференциальные уравнения 59, no. 6 (June 15, 2023): 843–46. http://dx.doi.org/10.31857/s0374064123060134.

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In even-dimensional phase spaces, we give examples of analytic systems of differential equations that have isolated equilibria and admit nonanalytic first integrals. These integrals are positive definite in a neighborhood of the equilibria, which proves the stability of the equilibria (on the entire time axis). However, such systems of differential equations do not admit nontrivial first integrals in the form of formal power series at all. In particular, the Lyapunov stability of equilibria of analytic systems does not imply their formal stability. In the case of an odd-dimensional phase space, all isolated equilibria are apparently unstable.

5

Gradwohl, Ronen, and Ehud Kalai. "Large Games: Robustness and Stability." Annual Review of Economics 13, no. 1 (August 5, 2021): 39–56. http://dx.doi.org/10.1146/annurev-economics-072720-042303.

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This review focuses on properties related to the robustness and stability of Nash equilibria in games with a large number of players. Somewhat surprisingly, these equilibria become substantially more robust and stable as the number of players increases. We illustrate the relevant phenomena through a binary-action game with strategic substitutes, framed as a game of social isolation in a pandemic environment.

6

KANSO, EVA, and BABAK GHAEMI OSKOUEI. "Stability of a coupled body–vortex system." Journal of Fluid Mechanics 600 (March 26, 2008): 77–94. http://dx.doi.org/10.1017/s0022112008000359.

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This paper considers the dynamics of a rigid body interacting with point vortices in a perfect fluid. The fluid velocity is obtained using the classical complex variables theory and conformal transformations. The equations of motion of the solid–fluid system are formulated in terms of the solid variables and the position of the point vortices only. These equations are applied to study the dynamic interaction of an elliptic cylinder with vortex pairs because of its relevance to understanding the swimming of fish in an ambient vorticity field. Two families of relative equilibria are found: moving Föppl equilibria; and equilibria along the ellipse's axis of symmetry (the axis perpendicular to the direction of motion). The two families of relative equilibria are similar to those present in the classical problem of flow past a fixed body, but their stability differs significantly from the classical ones.

7

Furi, M., M. Martelli, and M. O'Neill. "Global stability of equilibria." Journal of Difference Equations and Applications 15, no. 4 (April 2009): 387–97. http://dx.doi.org/10.1080/10236190802604383.

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8

Howard, James. "Stability of Hamiltonian equilibria." Scholarpedia 8, no. 10 (2013): 3627. http://dx.doi.org/10.4249/scholarpedia.3627.

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9

Giacobbe, Andrea, and Giuseppe Mulone. "Stability of ordered equilibria." Journal of Mathematical Analysis and Applications 462, no. 2 (June 2018): 1298–308. http://dx.doi.org/10.1016/j.jmaa.2018.02.040.

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10

Dritschel, David G. "Equilibria and stability of four point vortices on a sphere." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2241 (September 2020): 20200344. http://dx.doi.org/10.1098/rspa.2020.0344.

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This paper discusses the problem of finding the equilibrium positions of four point vortices, of generally unequal circulations, on the surface of a sphere. A random search method is developed which uses a modification of the linearized equations to converge on distinct equilibria. Many equilibria (47 and possibly more) may exist for prescribed circulations and angular impulse. A linear stability analysis indicates that they are generally unstable, though stable equilibria do exist. Overall, there is a surprising diversity of equilibria, including those which rotate about an axis opposite to the angular impulse vector.

11

Płotka, H., and D. G. Dritschel. "Simply-connected vortex-patch shallow-water quasi-equilibria." Journal of Fluid Mechanics 743 (March 5, 2014): 481–502. http://dx.doi.org/10.1017/jfm.2014.48.

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AbstractWe examine the form, properties, stability and evolution of simply-connected vortex-patch relative quasi-equilibria in the single-layer $f$-plane shallow-water model of geophysical fluid dynamics. We examine the effects of the size, shape and strength of vortices in this system, represented by three distinct parameters completely describing the families of the quasi-equilibria. Namely, these are the ratio $\gamma = L/L_D$ between the horizontal size of the vortices and the Rossby deformation length; the aspect ratio $\lambda $ between the minor to major axes of the vortex; and a potential vorticity (PV)-based Rossby number $\mathit{Ro}= q^{\prime }/f$, the ratio of the PV anomaly $q^{\prime }$ within the vortex to the Coriolis frequency $f$. By defining an appropriate steadiness parameter, we find that the quasi-equilibria remain steady for long times, enabling us to determine the boundary of stability $\lambda _c=\lambda _c(\gamma ,\mathit{Ro})$, for $0.25 \leq \gamma \leq 6$ and $\delimiter "026A30C \mathit{Ro}\delimiter "026A30C \leq 1$. By calling two states which share $\gamma ,\delimiter "026A30C \mathit{Ro}\delimiter "026A30C $ and $\lambda $ ‘equivalent’, we find a clear asymmetry in the stability of cyclonic ($\mathit{Ro}> 0$) and anticyclonic ($\mathit{Ro}<0$) equilibria, with cyclones being able to sustain greater deformations than anticyclones before experiencing an instability. We find that ageostrophic motions stabilise cyclones and destabilise anticyclones. Both types of vortices undergo the same main types of unstable evolution, albeit in different ranges of the parameter space, (a) vacillations for large-$\gamma $, large-$\mathit{Ro}$ states, (b) filamentation for small-$\gamma $ states and (c) vortex splitting, asymmetric for intermediate-$\gamma $ and symmetric for large-$\gamma $ states.

12

Morrison, P. J. "Variational Principle and Stability of Nonmonotonic Vlasov-Poisson Equilibria." Zeitschrift für Naturforschung A 42, no. 10 (October 1, 1987): 1115–23. http://dx.doi.org/10.1515/zna-1987-1009.

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The stability of nonmonotonic equilibria of the Vlasov-Poisson equation is assessed by using nonlinear constants of motion . The constants of motion make up the free energy of the system , which upon variation yields nonmonotonic equilibria. Such equilibria have not previously been obtainable from a variation principle, but here this is accomplished by the inclusion of a passively advected tracer field. Definiteness of the second variation of the free energy gives a sufficient condition for stability in agreement with Gardner’s theorem [5], Previously, we have argued that indefiniteness implies either spectral in stability or negative energy modes, which are generically unstable when one adds dissipation or nonlinearity [6]. Such is the case for the nonmonotonic equilibria considered.

13

Sun, Hai Ting, and Yuan Tian. "Continuously Harvesting of a Phytoplankton-Zooplankton System with Holling I Functional Response." Applied Mechanics and Materials 595 (July 2014): 277–82. http://dx.doi.org/10.4028/www.scientific.net/amm.595.277.

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In this paper, continuously harvesting of a phytoplankton-zooplankton system with Holling I functional response is proposed and analyzed. Firstly, the existence and stability of equilibria are addressed; the global asymptotical stability of equilibria is investigated by the Lyapunov method. And then, the existence of bionomic equilibria and the optimal harvesting policy are discussed. Finally, the conclusion is given.

14

Christev, Atanas, and Sergey Slobodyan. "LEARNABILITY OF E–STABLE EQUILIBRIA." Macroeconomic Dynamics 18, no. 5 (April 3, 2013): 959–84. http://dx.doi.org/10.1017/s1365100512000703.

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If private sector agents update their beliefs with a learning algorithm other than recursive least squares, expectational stability or learnability of rational expectations equilibria (REE) is not guaranteed. Monetary policy under commitment, with a determinate and E-stable REE, may not imply robust learning stability of such equilibria if the RLS speed of convergence is slow. In this paper, we propose a refinement of E-stability conditions that allows us to select equilibria more robust to specification of the learning algorithm within the RLS/SG/GSG class. E-stable equilibria characterized by faster speed of convergence under RLS learning are learnable with SG or generalized SG algorithms as well.

15

Duncan, William, and Tomas Gedeon. "Stability and Bifurcations of Equilibria in Networks with Piecewise Linear Interactions." International Journal of Bifurcation and Chaos 31, no. 11 (September 2, 2021): 2130032. http://dx.doi.org/10.1142/s0218127421300329.

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In this paper, we study equilibria of differential equation models for networks. When interactions between nodes are taken to be piecewise constant, an efficient combinatorial analysis can be used to characterize the equilibria. When the piecewise constant functions are replaced with piecewise linear functions, the equilibria are preserved as long as the piecewise linear functions are sufficiently steep. Therefore the combinatorial analysis can be leveraged to understand a broader class of interactions. To better understand how broad this class is, we explicitly characterize how steep the piecewise linear functions must be for the correspondence between equilibria to hold. To do so, we analyze the steady state and Hopf bifurcations which cause a change in the number or stability of equilibria as slopes are decreased. Additionally, we show how to choose a subset of parameters so that the correspondence between equilibria holds for the smallest possible slopes when the remaining parameters are fixed.

16

CAŞU, IOAN. "ON THE STABILITY PROBLEM FOR THE $\mathfrak{so}(5)$ FREE RIGID BODY." International Journal of Geometric Methods in Modern Physics 08, no. 06 (September 2011): 1205–23. http://dx.doi.org/10.1142/s0219887811005610.

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In the general case of the [Formula: see text] free rigid body, we will give a list of integrals of motion, which generate the set of Mishchenko's integrals. In the case of [Formula: see text], we prove that there are 15 coordinate-type Cartan subalgebras which on a regular adjoint orbit give 15 Weyl group orbits of equilibria. These coordinate-type Cartan subalgebras are the analogs of the three axes of equilibria for the classical rigid body on [Formula: see text]. The nonlinear stability and instability of these equilibria is analyzed. In addition to these equilibria there are 10 other continuous families of equilibria.

17

CURRAN, P. F., and L. O. CHUA. "STABILITY OF EQUILIBRIA OF NEURAL NETWORKS." International Journal of Bifurcation and Chaos 09, no. 10 (October 1999): 1941–55. http://dx.doi.org/10.1142/s0218127499001413.

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Sufficient conditions for local and global asymptotic stability of equilibria of some general classes of neural networks are presented. In the event that the interconnection matrix is block diagonally stable it is shown that the equilibrium is globally asymptotically stable if the cells are dissipative at the equilibrium. For a special class of networks the conditions of dissipativity are reduced to more readily-tested conditions of passivity. Equilibria are shown to be asymptotically stable essentially if the cells are locally passive.

18

Yang, Qigui, and Xinmei Qiao. "Constructing a New 3D Chaotic System with Any Number of Equilibria." International Journal of Bifurcation and Chaos 29, no. 05 (May 2019): 1950060. http://dx.doi.org/10.1142/s0218127419500603.

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In the chaotic polynomial Lorenz-type systems (including Lorenz, Chen, Lü and Yang systems) and Rössler system, their equilibria are unstable and the number of the hyperbolic equilibria are no more than three. This paper shows how to construct a simple analytic (nonpolynomial) chaotic system that can have any preassigned number of equilibria. A special 3D chaotic system with no equilibrium is first presented and discussed. Using a methodology of adding a constant controller to the third equation of such a chaotic system, it is shown that a chaotic system with any preassigned number of equilibria can be generated. Two complete mathematical characterizations for the number and stability of their equilibria are further rigorously derived and studied. This system is very interesting in the sense that some complex dynamics are found, revealing many amazing properties: (i) a hidden chaotic attractor exists with no equilibria or only one stable equilibrium; (ii) the chaotic attractor coexists with unstable equilibria, including two/five unstable equilibria; (iii) the chaotic attractor coexists with stable equilibria and unstable equilibria, including one stable and two unstable equilibria/94 stable and 93 unstable equilibria; (iv) the chaotic attractor coexists with infinitely many nonhyperbolic isolated equilibria. These results reveal an intrinsic relationship of the global dynamical behaviors with the number and stability of the equilibria of some unusual chaotic systems.

19

Tahir, Muhammad, Syed Shah, Gul Zaman, and Tahir Khan. "Stability behaviour of mathematical model MERS corona virus spread in population." Filomat 33, no. 12 (2019): 3947–60. http://dx.doi.org/10.2298/fil1912947t.

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In this subsection, we first formulated the proposed model in there infectious classes and then we derived the basic key value reproductive number, R0 with the help of next generation approach. Then we obtained all the endemic equilibrium points, as well as, local stability analysis, at disease free equilibria and, at endemic equilibria of the related model and shown stable. Further the global stability analysis either, at disease free equilibria, and at endemic equilibria is discussed by constructing Lyapunov function which show the validity of the concern model exist. In the last part of the article numerical simulation is presented for the model which support the model existence with the help of RK-4 method.

20

Świtalski, Zbigniew. "Stability and Price Equilibria in a Many-to-Many Gale-Shapley Market Model." Przegląd Statystyczny 64, no. 3 (September 30, 2017): 229–48. http://dx.doi.org/10.5604/01.3001.0014.0807.

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In the paper we study relationships between generalized competitive equilibria defined in the paper of Świtalski (2016) and price equilibria for some variant of many-to-many market model of Gale- Shapley type and between price equilibria and stable matchings for such a model. Obtained results are used for proving theorems on existence of price equilibria in the many-to-many GS-model and in the many-to-many model generalizing the model of Chen, Deng and Ghosh (Chen et al., 2014).

21

Sukhov, E. A., and E. V. Volkov. "Numerical Orbital Stability Analysis of Nonresonant Periodic Motions in the Planar Restricted Four-Body Problem." Nelineinaya Dinamika 18, no. 4 (2022): 0. http://dx.doi.org/10.20537/nd221201.

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We address the planar restricted four-body problem with a small body of negligible mass moving in the Newtonian gravitational field of three primary bodies with nonnegligible masses. We assume that two of the primaries have equal masses and that all primary bodies move in circular orbits forming a Lagrangian equilateral triangular configuration. This configuration admits relative equilibria for the small body analogous to the libration points in the three-body problem. We consider the equilibrium points located on the perpendicular bisector of the Lagrangian triangle in which case the bodies constitute the so-called central configurations. Using the method of normal forms, we analytically obtain families of periodic motions emanating from the stable relative equilibria in a nonresonant case and continue them numerically to the borders of their existence domains. Using a numerical method, we investigate the orbital stability of the aforementioned periodic motions and represent the conclusions as stability diagrams in the problem’s parameter space.

22

Harper, A. B. "Evolutionary Stability for Interactions among Kin under Quantitative Inheritance." Genetics 121, no. 4 (April 1, 1989): 877–89. http://dx.doi.org/10.1093/genetics/121.4.877.

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Abstract The theory of evolutionarily stable strategies (ESS) predicts the long-term evolutionary outcome of frequency-dependent selection by making a number of simplifying assumptions about the genetic basis of inheritance. I use a symmetrized multilocus model of quantitative inheritance without mutation to analyze the results of interactions between pairs of related individuals and compare the equilibria to those found by ESS analysis. It is assumed that the fitness changes due to interactions can be approximated by the exponential of a quadratic surface. The major results are the following. (1) The evolutionarily stable phenotypes found by ESS analysis are always equilibria of the model studied here. (2) When relatives interact, one of the two conditions for stability of equilibria differs between the two models; this can be accounted for by positing that the inclusive fitness function for quantitative characters is slightly different from the inclusive fitness function for characters determined by a single locus. (3) The inclusion of environmental variance will in general change the equilibrium phenotype, but the equilibria of ESS analysis are changed to the same extent by environmental variance. (4) A class of genetically polymorphic equilibria occur, which in the present model are always unstable. These results expand the range of conditions under which one can validly predict the evolution of pairwise interactions using ESS analysis.

23

Luo, Demou, and Qiru Wang. "Global Dynamics of a Holling-II Amensalism System with Nonlinear Growth Rate and Allee Effect on the First Species." International Journal of Bifurcation and Chaos 31, no. 03 (March 15, 2021): 2150050. http://dx.doi.org/10.1142/s0218127421500504.

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Of concern is the global dynamics of a two-species Holling-II amensalism system with nonlinear growth rate. The existence and stability of trivial equilibrium, semi-trivial equilibria, interior equilibria and infinite singularity are studied. Under different parameters, there exist two stable equilibria which means that this model is not always globally asymptotically stable. Together with the existence of all possible equilibria and their stability, saddle connection and close orbits, we derive some conditions for transcritical bifurcation and saddle-node bifurcation. Furthermore, the global dynamics of the model is performed. Next, we incorporate Allee effect on the first species and offer a new analysis of equilibria and bifurcation discussion of the model. Finally, several numerical examples are performed to verify our theoretical results.

24

ÇAY, İrem. "Stability of an SIRS Epidemic Model with Saturated Incidence Rate and Saturated Treatment Function." Journal of Mathematical Sciences and Modelling 4, no. 3 (December 27, 2021): 133–38. http://dx.doi.org/10.33187/jmsm.1009561.

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In this paper the global dynamics of susceptible-infected-recovered-susceptible (SIRS) epidemic model with saturated incidence rate and saturated treatment function is studied. Firstly, the basic reproduction number $R_0$ is calculated and the existence of the disease-free and positive equilibria is showed. In addition, local stability of the equilibria is investigated. Then, sufficient conditions are achieved for global stability of disease-free and endemic equilibria. Finally, the numerical examples are presented to validate the theoretical results.

25

LU, ZHIQI, and JINGJING WU. "GLOBAL STABILITY OF A CHEMOSTAT MODEL WITH DELAYED RESPONSE IN GROWTH AND A LETHAL EXTERNAL INHIBITOR." International Journal of Biomathematics 01, no. 04 (December 2008): 503–20. http://dx.doi.org/10.1142/s1793524508000436.

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A competition model between two species with a lethal inhibitor in a chemostat is analyzed. Discrete delays are used to describe the nutrient conversion process. The proved qualitative properties of the solution are positivity, boundedness. By analyzing the local stability of equilibria, it is found that the conditions for stability and instability of the boundary equilibria are similar to those in [9]. In addition, the global asymptotic behavior of the system is discussed and the sufficient conditions for the global stability of the boundary equilibria are obtained. Moreover, by numerical simulation, it is interesting to find that the positive equilibrium may be globally stable.

26

Howitt, Peter, and R. Preston McAfee. "Stability of Equilibria with Externalities." Quarterly Journal of Economics 103, no. 2 (May 1988): 261. http://dx.doi.org/10.2307/1885112.

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27

Ortega, Juan-Pablo, and Tudor S. Ratiu. "Stability of Hamiltonian relative equilibria." Nonlinearity 12, no. 3 (January 1, 1999): 693–720. http://dx.doi.org/10.1088/0951-7715/12/3/315.

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28

Vasin, Alexander. "On stability of mixed equilibria." Nonlinear Analysis: Theory, Methods & Applications 38, no. 6 (December 1999): 793–802. http://dx.doi.org/10.1016/s0362-546x(98)00154-0.

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29

Howard, James E. "Spectral stability of relative equilibria." Celestial Mechanics & Dynamical Astronomy 48, no. 3 (September 1990): 267–88. http://dx.doi.org/10.1007/bf02524333.

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30

Liu, L. P. "Stability Analysis of Dynamic Equilibria." Journal of Mathematical Analysis and Applications 193, no. 3 (August 1995): 800–816. http://dx.doi.org/10.1006/jmaa.1995.1268.

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31

Cripps, Martin. "Correlated equilibria and evolutionary stability." Journal of Economic Theory 55, no. 2 (December 1991): 428–34. http://dx.doi.org/10.1016/0022-0531(91)90048-9.

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32

Dijkstra, Henk A., and Wilbert Weijer. "Stability of the Global Ocean Circulation: Basic Bifurcation Diagrams." Journal of Physical Oceanography 35, no. 6 (June 1, 2005): 933–48. http://dx.doi.org/10.1175/jpo2726.1.

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Abstract A study of the stability of the global ocean circulation is performed within a coarse-resolution general circulation model. Using techniques of numerical bifurcation theory, steady states of the global ocean circulation are explicitly calculated as parameters are varied. Under a freshwater flux forcing that is diagnosed from a reference circulation with Levitus surface salinity fields, the global ocean circulation has no multiple equilibria. It is shown how this unique-state regime transforms into a regime with multiple equilibria as the pattern of the freshwater flux is changed in the northern North Atlantic Ocean. In the multiple-equilibria regime, there are two branches of stable steady solutions: one with a strong northern overturning in the Atlantic and one with hardly any northern overturning. Along the unstable branch that connects both stable solution branches (here for the first time computed for a global ocean model), the strength of the southern sinking in the South Atlantic changes substantially. The existence of the multiple-equilibria regime critically depends on the spatial pattern of the freshwater flux field and explains the hysteresis behavior as found in many previous modeling studies.

33

Shakhmurov, Veli B., Muhammet Kurulay, Aida Sahmurova, Mustafa Can Gursesli, and Antonio Lanata. "A Novel Nonlinear Dynamic Model Describing the Spread of Virus." Mathematics 11, no. 20 (October 10, 2023): 4226. http://dx.doi.org/10.3390/math11204226.

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This study proposes a nonlinear mathematical model of virus transmission. The interaction between viruses and immune cells is investigated using phase-space analysis. Specifically, the work focuses on the dynamics and stability behavior of the mathematical model of a virus spread in a population and its interaction with human immune system cells. The endemic equilibrium points are found, and local stability analysis of all equilibria points of the related model is obtained. Further, the global stability analysis, either at disease-free equilibria or in endemic equilibria, is discussed by constructing the Lyapunov function, which shows the validity of the concern model. Finally, a simulated solution is achieved, and the relationship between viruses and immune cells is highlighted.

34

Krasilnikov, P. S., and A. R. Ismagilov. "On the Dumb-Bell Equilibria in the Generalized Sitnikov Problem." Nelineinaya Dinamika 18, no. 4 (2022): 0. http://dx.doi.org/10.20537/nd221203.

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We also investigate the linear stability of the trivial equilibrium of a symmetrical dumb–bell in the elliptic Sitnikov problem. In the case of the dumb–bell length $l\geq 0.983819$, an instability of the trivial equilibria for eccentricity $e\in(0,1)$ is proved.

35

Baez Sanchez, A. D., and N. Bobko. "On Equilibria Stability in an Epidemiological SIR Model with Recovery-dependent Infection Rate." TEMA (São Carlos) 21, no. 3 (November 27, 2020): 409. http://dx.doi.org/10.5540/tema.2020.021.03.409.

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We consider an epidemiological SIR model with an infection rate depending on the recovered population. We establish sufficient conditions for existence, uniqueness, and stability (local and global) of endemic equilibria and consider also the stability of the disease-free equilibrium. We show that, in contrast with classical SIR models, a system with a recovery-dependent infection rate can have multiple endemic stable equilibria (multistability) and multiple stable and unstable saddle points of equilibria. We establish conditions for the occurrence of these phenomena and illustrate the results with some examples.

36

Carvalho dos Santos, José Paulo, Evandro Monteiro, José Claudinei Ferreira, Nelson Henrique Teixeira Lemes, and Diego Samuel Rodrigues. "Well-posedness and qualitative analysis of a SEIR model with spatial diffusion for COVID-19 spreading." BIOMATH 12, no. 1 (July 28, 2023): 2307207. http://dx.doi.org/10.55630/j.biomath.2023.07.207.

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In this paper, we study the well-posedness and the qualitative behavior of equilibria of a SEIR epidemic models with spatial diffusion for the spreading of COVID-19. The well-posedness of the model is proved using both the Semigroup Theory of sectorial operators and existence results for abstract parabolic differential equations. The asymptotical local stability of both disease-free and endemic equilibria are established using standard linearization theory, and confirmed by illustrative numerical simulations. The asymptotical global stability of both disease-free and endemic equilibria are established using a Lyapunov function.

37

Wang, Tieying. "Microbial insecticide model and homoclinic bifurcation of impulsive control system." International Journal of Biomathematics 14, no. 06 (July 1, 2021): 2150043. http://dx.doi.org/10.1142/s1793524521500431.

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A new microbial insecticide mathematical model with density dependent for pest is proposed in this paper. First, the system without impulsive state feedback control is considered. The existence and stability of equilibria are investigated and the properties of equilibria under different conditions are verified by using numerical simulation. Since the system without pulse has two positive equilibria under some additional assumptions, the system is not globally asymptotically stable. Based on the stability analysis of equilibria, limit cycle, outer boundary line and Sotomayor’s theorem, the existence of saddle-node bifurcation and global dynamics of the system are obtained. Second, we consider homoclinic bifurcation of the system with impulsive state feedback control. The existence of order-1 homoclinic orbit of the system is studied. When the impulsive function is slightly disturbed, the homoclinic orbit breaks and bifurcates order-1 periodic solution. The existence and stability of order-1 periodic solution are obtained by means of theory of semi-continuous dynamic system.

38

Yang, Shengxu. "Regional Stability of Switching Control Circuit Systems with Multiple Equilibria." Journal of Physics: Conference Series 2355, no. 1 (October 1, 2022): 012027. http://dx.doi.org/10.1088/1742-6596/2355/1/012027.

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Abstract This paper investigates the stability of systems of multi-equilibrium switching circuits. For a first-order switching circuit system with two subsystems containing unique equilibria and different equilibria, we first establish a sufficient condition for the stability of the region of the multi-equilibrium first-order switching circuit system, and then complete the proof of its stability by means of a general solution of the system state. Secondly, for the second-order multi-equilibrium switching circuit system, the sufficient condition for the stability of the second-order multi-equilibrium switching circuit system is given, and the feasibility of the theorem is finally proved by drawing on existing research results and related sufficient conditions. The conclusions obtained show that the system of first- and second-order multiple equilibria switching circuits in the region is regionally stable after the corresponding switching paths.

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Georgescu, Paul, та Hong Zhang. "Facultative Mutualisms and θ-Logistic Growth: How Larger Exponents Promote Global Stability of Co-Existence Equilibria". Mathematics 11, № 20 (21 жовтня 2023): 4373. http://dx.doi.org/10.3390/math11204373.

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We investigate the stability of co-existence equilibria for two-species models of facultative mutualism for which birth and death are modeled as separate processes, with possibly distinct types of density dependence, and the mutualistic contributions are either linear or saturating. To provide a unifying perspective, we first introduce and discuss a generic stability framework, finding sufficient stability conditions expressed in terms of reproductive numbers computed at high population densities. To this purpose, an approach based on the theory of monotone dynamical systems is employed. The outcomes of the generic stability framework are then used to characterize the dynamics of the two-species models of concern, delineating between decelerating (lower-powered) and accelerating (higher-powered) density dependences. It is subsequently seen that accelerating density dependences promote the stability of co-existence equilibria, while decelerating density dependences either completely destabilize the system via promoting the unboundedness of solutions or create multiple co-existence equilibria.

40

Kang, Aihua, Yakui Xue, and Jianping Fu. "Dynamic Behaviors of a Leslie-Gower Ecoepidemiological Model." Discrete Dynamics in Nature and Society 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/169242.

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A Leslie-Gower ecoepidemic model with disease in the predators is constructed and analyzed. The total population is subdivided into three subclasses, namely, susceptible predator, infected predator, and prey population. The positivity, boundness of solutions, and the existence of the equilibria are studied, and the sufficient conditions of local asymptotic stability of the equilibria are obtained by the Routh-Hurwitz criterion. We analyze the global stability of the interior equilibria by using Lyapunov functions. It is observed that a Hopf bifurcation may occur around the interior equilibrium. At last, numeric simulations are performed in support of the feasibility of the main result.

41

Alós-Ferrer, Carlos. "Finite Population Dynamics and Mixed Equilibria." International Game Theory Review 05, no. 03 (September 2003): 263–90. http://dx.doi.org/10.1142/s0219198903001057.

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This paper examines the stability of mixed-strategy Nash equilibria of symmetric games, viewed as population profiles in dynamical systems with learning within a single, finite population. Alternative models of imitation and myopic best reply are considered under different assumptions on the speed of adjustment. It is found that two specific refinements of mixed Nash equilibria identify focal rest points of these dynamics in general games. The relationship between both concepts is studied. In the 2×2 case, both imitation and myopic best reply yield strong stability results for the same type of mixed Nash equilibria.

42

Schoof, Christian. "Marine ice sheet stability." Journal of Fluid Mechanics 698 (March 15, 2012): 62–72. http://dx.doi.org/10.1017/jfm.2012.43.

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AbstractWe examine the stability of two-dimensional marine ice sheets in steady state. The dynamics of marine ice sheets is described by a viscous thin-film model with two Stefan-type boundary conditions at the moving boundary or ‘grounding line’ that marks the transition from grounded to floating ice. One of these boundary conditions constrains ice thickness to be at a local critical value for flotation, which depends on depth to bedrock at the grounding line. The other condition sets ice flux as a function of ice thickness at the grounding line. Depending on the shape of the bedrock, multiple equilibria may be possible. Using a linear stability analysis, we confirm a long-standing heuristic argument that asserts that the stability of these equilibria is determined by a simple mass balance consideration. If an advance in the grounding line away from its steady-state position leads to a net mass gain, the steady state is unstable, and stable otherwise. This also confirms that grounding lines can only be stable in positions where bedrock slopes downwards sufficiently steeply.

43

Ji, Yangyang, and Wei Xiao. "INSTABILITY OF SUNSPOT EQUILIBRIA IN REAL BUSINESS CYCLE MODELS UNDER INFINITE HORIZON LEARNING." Macroeconomic Dynamics 22, no. 8 (December 2018): 1978–2006. http://dx.doi.org/10.1017/s1365100516000973.

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This paper examines the stability of sunspot equilibria in one-sector RBC models under infinite horizon learning. We present general conditions under which the reduced-form model can possess E-stable sunspot equilibria and apply these conditions to three prominent one-sector RBC models. We find that the rational expectations sunspot equilibria are generally unstable under learning.

44

Fey, Mark. "Stability and Coordination in Duverger's Law: A Formal Model of Preelection Polls and Strategic Voting." American Political Science Review 91, no. 1 (March 1997): 135–47. http://dx.doi.org/10.2307/2952264.

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This paper investigates the dynamics of the “wasted vote” phenomenon and Duverger's Law. I construct a theoretical model in order to consider how preelection polls serve to inform the electorate about the relative chances of the candidates and how that information acts over time to decrease the support of the trailing candidate. The results shed light on how public opinion polls can aggregate information in the electorate and coordinate voters on the viable candidates in the election. Specifically, I show that in a Bayesian game model of strategic voting there exist non-Duvergerian equilibria in which all three candidates receive votes (in the limit). These equilibria require extreme coordination, however, and any variation in beliefs leads voters away from them to one of the Duvergerian equilibria. Thus, non-Duvergerian equilibria are unstable, while two-party equilibria are not. In addition, I describe how preelection polls provide information to voters about the viability of candidates and can thus be used by voters to coordinate on a Duvergerian outcome.

45

Schamel, H. "On the Stability of Localized Electrostatic Structures." Zeitschrift für Naturforschung A 42, no. 10 (October 1, 1987): 1167–74. http://dx.doi.org/10.1515/zna-1987-1015.

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46

PARDO, OLIVIER. "GLOBAL STABILITY FOR A PHYTOPLANKTON-NUTRIENT SYSTEM." Journal of Biological Systems 08, no. 02 (June 2000): 195–209. http://dx.doi.org/10.1142/s0218339000000122.

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The model proposed by A. H. Taylor et al. [18] is discussed, with a view to determining the global asymptotic stability of the equilibria. The system consists of two autonomous differential equations, modeling the couple Phytoplankton-Nutrient with no delay on the recycling efficiency of nutrient by bacterial decomposition. Two distinct cases, persistence and extinction of phytoplankton are considered. In each case we will state the local and then the global stability of the equilibria by constructing an appropriate Lyapunov function and using the LaSalle's invariance principle. Also, in the case of extinction of phytoplankton we have introduced a supply of nutrient in the system and we have revealed the bloom of phytoplankton, which appears biologically in upwelling conditions.

47

Parsamanesh, Mahmood, and Saeed Mehrshad. "Stability of the equilibria in a discrete-time sivs epidemic model with standard incidence." Filomat 33, no. 8 (2019): 2393–408. http://dx.doi.org/10.2298/fil1908393p.

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A discrete-time SIS epidemic model with vaccination is presented and studied. The model includes deaths due to disease and the total population size is variable. First, existence and positivity of the solutions are discussed and equilibria of the model and basic reproduction number are obtained. Next, the stability of the equilibria is studied and conditions of stability are obtained in terms of the basic reproduction number R0. Also, occurrence of the fold bifurcation, the flip bifurcation, and the Neimark-Sacker bifurcation is investigated at equilibria. In addition, obtained results are numerically discussed and some diagrams for bifurcations, Lyapunov exponents, and solutions of the model are presented.

48

Faghihi, M., and J. Scheffel. "Stability of short-axial-wavelength internal kink modes of an anisotropic plasma." Journal of Plasma Physics 38, no. 3 (December 1987): 495–99. http://dx.doi.org/10.1017/s0022377800012769.

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The double adiabatic equations are used to study the stability of a cylindrical Z-pinch with respect to small axial wavelength, internal kink (m ≥ 1) modes. It is found that marginally (ideally) unstable, isotropic equilibria are stabilized. Also, constant-current-density equilibria can be stabilized for P⊥ > P∥ and large β⊥

49

Fleiner, Tamás, Ravi Jagadeesan, Zsuzsanna Jankó, and Alexander Teytelboym. "Trading Networks With Frictions." Econometrica 87, no. 5 (2019): 1633–61. http://dx.doi.org/10.3982/ecta14159.

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We show how frictions and continuous transfers jointly affect equilibria in a model of matching in trading networks. Our model incorporates distortionary frictions such as transaction taxes and commissions. When contracts are fully substitutable for firms, competitive equilibria exist and coincide with outcomes that satisfy a cooperative solution concept called trail stability. However, competitive equilibria are generally neither stable nor Pareto‐efficient.

50

Kholostova, O. V. "Nonlinear Stability Analysis of Relative Equilibria of a Solid Carrying a Movable Point Mass in the Central Gravitational Field." Nelineinaya Dinamika 15, no. 4 (2019): 505–12. http://dx.doi.org/10.20537/nd190409.

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