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1
Fragnelli, Genni. "Delay equations with nonautonomous past". [S.l. : s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=963845691.
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Luís, Rafael Domingos Garanito. "Nonautonomous difference equations with applications". Doctoral thesis, Universidade da Madeira, 2011. http://hdl.handle.net/10400.13/206.
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This work is divided in two parts. In the first part we develop the theory of discrete nonautonomous dynamical systems. In particular, we investigate skew-product dynamical system, periodicity, stability, center manifold, and bifurcation.
In the second part we present some concrete models that are used in ecology/biology and
economics. In addition to developing the mathematical theory of these models, we use simulations to construct graphs that illustrate and describe the dynamics of the models.
One of the main contributions of this dissertation is the study of the stability of some concrete nonlinear maps using the center manifold theory. Moreover, the second contribution is the study of bifurcation, and in particular the construction of bifurcation diagrams in the parameter
space of the autonomous Ricker competition model.
Since the dynamics of the Ricker competition model is similar to the logistic competition
model, we believe that there exists a certain class of two-dimensional maps with which we can generalize our results.
Finally, using the Brouwer’s fixed point theorem and the construction of a compact invariant and convex subset of the space, we present a proof of the existence of a positive periodic solution of the nonautonomous Ricker competition model.Henrique Oliveira and Saber Elaydi
3
Cuendet, Michel Alain. "Aspects of thermostated and nonautonomous molecular dynamics /". Zürich : ETH, 2006. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=16863.
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Shchetinina, Ekaterina. "Integral manifolds for nonautonomous slow fast systems without dichotomy". Doctoral thesis, [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=972647600.
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Kobayashi, Tadashi. "Study of Autonomous and Nonautonomous Higher Dimensional Integrable Equations". 京都大学 (Kyoto University), 2012. http://hdl.handle.net/2433/157480.
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Altemeier, Daniel [Verfasser] y Barbara [Akademischer Betreuer] Gentz. "Concentration Inequalities for Nonautonomous Stochastic Delay Differential Equations / Daniel Altemeier ; Betreuer: Barbara Gentz". Bielefeld : Universitätsbibliothek Bielefeld, 2017. http://d-nb.info/1150182024/34.
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Alkhayuon, Hassan Mazin. "Rate-induced transitions for parameter shift systems". Thesis, University of Exeter, 2018. http://hdl.handle.net/10871/35071.
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Rate-induced transitions have recently emerged as an identifiable type of instability of attractors in nonautonomous dynamical systems. In most studies so far, these attractors can be associated with equilibria of an autonomous limiting system, but this is not necessarily the case. For a specific class of systems with a parameter shift between two autonomous systems, we consider how the breakdown of the quasistatic approximation for attractors can lead to rate-induced transitions, where nonautonomous instability can be characterised in terms of a critical rate of the parameter shift. We find a number of new phenomena for non-equilibrium attractors: weak tracking where the pullback attractor of the system limits to a proper subset of the attractor of the future limit system, partial tipping where certain phases of the pullback attractor tip and others track the quasistatic attractor, em invisible tipping where the critical rate of partial tipping is isolated and separates two parameter regions where the system exhibits end-point tracking. For a model parameter shift system with periodic attractors, we characterise thresholds of rate-induced tipping to partial and total tipping. We show these thresholds can be found in terms of certain periodic-to-periodic and periodic-to-equilibrium connections that we determine using Lin's method for an augmented system. Considering weak tracking for a nonautonomous Rossler system, we show that there are infinitely many critical rates at which a pullback attracting solution of the system tracks an embedded unstable periodic orbit of the future chaotic attractor.
8
Eisenmann, Monika [Verfasser], Etienne [Akademischer Betreuer] Emmrich, Etienne [Gutachter] Emmrich, Raphael [Gutachter] Kruse y Mechthild [Gutachter] Thalhammer. "Methods for the temporal approximation of nonlinear, nonautonomous evolution equations / Monika Eisenmann ; Gutachter: Etienne Emmrich, Raphael Kruse, Mechthild Thalhammer ; Betreuer: Etienne Emmrich". Berlin : Technische Universität Berlin, 2019. http://d-nb.info/1201725011/34.
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Silva, Maria Teresa Morais de Paiva Martins e. "Equilíbrio e taxas de convergência em sistemas dinâmicos discretos não autónomos". Doctoral thesis, Universidade de Évora, 2015. http://hdl.handle.net/10174/18209.
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Na primeira parte deste trabalho estudamos a convergência para a distribuição de equilíbrio em grafos não autónomos periódicos. Introduzimos a noção de equilíbrio em grafos não autónomos e apresentamos uma estimativa superior para a distância ao equilíbrio, `a custa do segundo valor próprio em módulo das matrizes produto, supondo todas as matrizes erg´odicas e pelo menos uma delas reversível. A estimativa obtida depende explicitamente da dimensão das matrizes consideradas. Estabelecemos a relação entre grafos autónomos e cadeias de Markov não homogéneas. Ilustramos, com um exemplo, a aplicação a sistemas dinâmicos não autónomos. Estendemos o estudo a matrizes n˜ao reversíveis demonstrando um resultado análogo ao caso reversível, no contexto autónomo e não autónomo, que utiliza a factorização da matriz através da forma normal de Jordan. Finalmente discutimos a pertinência dos resultados originais obtidos comparando-os com resultados conhecidos. Esta parte corresponde aos capítulos 2 e 3. A segunda parte, capítulo 4, ´e dedicada ao estudo detalhado de uma família de sistemas não autónomos de período 2, gerados pela iteração sequencial de duas funções do tipo tenda cortada. Apresentamos os conceitos de dinâmica simbólica, renormalização e produto estrela no contexto não autónomo, com o objectivo de calcular a taxa de convergência de sucessões de pontos no espaço de parâmetros, construidas através de produtos estrela/renormalizaçõesconsecutivas, generalizando assim as sequências de Feigenbaum. Concluímos que as taxas de convergência são independentes do ponto inicial, mostrando assim que o contexto não autónomo exibe propriedades universais do tipo encontrado por Feigenbaum em famílias de sistemas autónomos; Abstract: In the first part of this thesis we study the convergence for the equilibrium distribution in periodic non autonomous graphs. We introduce the notion of equilibrium in non autonomous graphs and give an upper bound for the distance to the equilibrium, using the second largest eigenvalue in modulus of the product matrices, assuming all of them ergodic and, at least, one reversible. The estimate obtained depends explicitly on the dimension of the considered matrices. We set the relation between non autonomous graphs and non homogeneous Markov chains. We illustrate the applications to the non autonomous dynamical systems with an example. We extend the study to non reversible matrices proving an analogous result, in both autonomous and non autonomous settings, using the matrix factorization with the Jordan normal form. Finally we discuss the relevance of the results obtained comparing them with the previously known results. This is the subject of chapters 2 and 3. The second part, chapter 4, is dedicated to studying a family of non autonomous systems with period 2, generated by the sequential iteration of two stunted sawtooth maps. We present the concepts of symbolic dynamics, renormalization and star product in the non autonomous setting, in order to compute the convergence rates of sequences of points in the parameter space. These sequences are obtained through consecutive star products/renormalizations, generalizing in this way the Feigenbaum sequences. We show that the convergence rates are independent of the initial point, thus, concluding that the non autonomous setting has universal properties of the type founded by Feigenbaum in families of autonomous systems.
10
Karrasch, Daniel. "Hyperbolicity & Invariant Manifolds for Finite-Time Processes". Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-97207.
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The aim of this thesis is to introduce a general framework for what is informally referred to as finite-time dynamics. Within this framework, we study hyperbolicity of reference trajectories, existence of invariant manifolds as well as normal hyperbolicity of invariant manifolds called Lagrangian Coherent Structures. We focus on a simple derivation of analytical results. At the same time, our approach together with the analytical results has strong impact on the numerical implementation by providing calculable expressions for known functions and continuity results that ensure robust computation. The main results of the thesis are robustness of finite-time hyperbolicity in a very general setting, finite-time analogues to classical linearization theorems, an approach to the computation of so-called growth rates and the generalization of the variational approach to Lagrangian Coherent Structures.
11
Lázaro, Heraclio Ledgar López [UNESP]. "Atratores pullback para equações parabólicas semilineares em domínios não cilíndricos". Universidade Estadual Paulista (UNESP), 2016. http://hdl.handle.net/11449/136350.
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
The problem that we are going to study in this work, is motivated by the dynamics of differential equations nonautonomous. We will establish the existence and uniqueness of solution for a class of parabolic semilineares equations with Dirichlet boundary condition, in a family of domains that varies with time. In addition, certain hypotheses about the non-linearity, we will show the existence of a family of attractors pullback.
O problema que vamos estudar neste trabalho é motivado pela dinâmica de equações diferenciais não autônomas. Vamos estabelecer a existência e unicidade de solução para uma classe de equaçõoes parabólicas semilineares com condição de fronteira de Dirichlet, em uma família de domínios que varia com o tempo. Além disso, sob certas hipóteses sobre a não linearidade, mostraremos a existência de uma família de atratores pullback.
12
Luu, Hoang Duc, Joseph Páez Chávez, Doan Thai Son y Stefan Siegmund. "Finite-time Lyapunov exponents and metabolic control coefficients for threshold detection of stimulus–response curves". Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-215920.
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In biochemical networks transient dynamics plays a fundamental role, since the activation of signalling pathways is determined by thresholds encountered during the transition from an initial state (e.g. an initial concentration of a certain protein) to a steady-state. These thresholds can be defined in terms of the inflection points of the stimulus-response curves associated to the activation processes in the biochemical network. In the present work, we present a rigorous discussion as to the suitability of finite-time Lyapunov exponents and metabolic control coefficients for the detection of inflection points of stimulus-response curves with sigmoidal shape.
13
Simões, Pedro Miguel Lola. "Dinâmica simbólica de aplicações multimodais renormalizáveis, renormalização em templates". Doctoral thesis, Universidade de Évora, 2015. http://hdl.handle.net/10174/16150.
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Este trabalho dedica-se à interpretação do conceito de renormalização em sistemas
dinâmicos não autónomos periódicos gerados pela iteração sequencial de aplicações do tipo
de Lorenz. Para tal socorremo-nos da dinâmica simbólica e do produto estrela sobre os
invariantes de amassamento.
Começamos por decompor o espaço de fases simbólico de sistemas renormalizáveis e em
seguida estudamos a entropia topológica destes sistemas restringidos aos intervalos de renormalização.
Finalmente, interpretamos estes conceitos no contexto dos templates com vários
segmentos de ramificação, obtendo uma descrição geométrica dos nós e elos correspondentes
a órbitas de pontos nos intervalos de renormalização e apresentando fórmulas explícitas para
o cálculo do genus destes nós e elos; ABSTRACT: Symbolic dynamics of renormalizable multimodal applications,
renormalization in templates
This work is dedicated to the interpretation of renormalization of periodic nonautonomous
dynamical systems generated by the sequential iteration of Lorenz like applications.
For this we use symbolic dynamics and star product on the kneading invariants.
We start by decomposing the symbolic phase space of renormalizable systems and then
we study the topological entropy of these systems restricted the renormalization intervals.
Finally, we interpret these concepts in the context of templates with multiple branching
segments, obtaining a geometric description of the knots and links corresponding to orbits
of points in renormalization intervals and featuring explicit formulas for calculating the
genus of these knots and links.
14
Hruboš, Zdeněk. "Oscilátory generující nekonvenční signály". Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2016. http://www.nusl.cz/ntk/nusl-239937.
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Dizertační práce se zabývá elektronicky nastavitelnými oscilátory, studiem nelineárních vlastností spojených s použitými aktivními prvky a posouzením možnosti vzniku chaotického signálu v harmonických oscilátorech. Jednotlivé příklady vzniku podivných atraktorů jsou detailně diskutovány. V doktorské práci je dále prezentováno modelování reálných fyzikálních a biologických systémů vykazujících chaotické chování pomocí analogových elektronických obvodů a moderních aktivních prvků (OTA, MO-OTA, CCII ±, DVCC ±, atd.), včetně experimentálního ověření navržených struktur. Další část práce se zabývá možnostmi v oblasti analogově – digitální syntézy nelineárních dynamických systémů, studiem změny matematických modelů a odpovídajícím řešením. Na závěr je uvedena analýza vlivu a dopadu parazitních vlastností aktivních prvků z hlediska kvalitativních změn v globálním dynamickém chování jednotlivých systémů s možností zániku chaosu v důsledku parazitních vlastností použitých aktivních prvků.
15
Lucas, Maxime. "Synchronisation and stability in nonautonomous oscillatory systems". Doctoral thesis, 2019. http://hdl.handle.net/2158/1155835.
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Many natural and artificial systems can be modelled by ensembles of coupled oscillators. These types of systems can exhibit various synchronisation phenomena, where the interaction between the oscillators leads them to some kind of coherent behaviour, despite heterogeneities in the system. Moreover, many such systems are subject to a timevariable environment which effectively drives them. Many examples can be found in living systems, e.g., the dynamics of a cell is strongly dependent on the ever-changing intra- and extra-cellular ionic concentrations.
Motivated by these considerations, this thesis investigates the effect of time-varying parameters on synchronisation and stability in ensembles of coupled oscillators. Timevariability is a crucial ingredient of the dynamics of many real-life systems, and interest in it is only recently starting to grow. Such systems are in general described by nonautonomous equations, which are hard to treat in general. This present work aims at answering questions such as: Can time-variability be detrimental/beneficial to synchronisation? If so, under which conditions? Can time-variability seed new dynamical phenomena? How can one best treat nonautonomous systems?
The systems studied can be divided into two categories. First, the effect of a driving oscillator with a time-varying frequency is investigated. It is shown that increasing the amplitude of the frequency modulation can increase the size of the stability region in parameter space, under general assumptions. Short-term dynamics and stability properties are also investigated, and their dynamics is shown to be of importance. Second, the effect of time-varying couplings between the oscillators is considered. This is shown to be able to make the synchronous state unstable and yield oscillation death.
Overall, the thesis illustrates that time-variability can be either beneficial or detrimental to synchronous dynamics, and investigates in detail and gives insight about cases of both. It argues towards the general fact that short-term dynamics is often crucial to a physically relevant understanding of nonautonomous systems.
16
Liao, Ming-Chou y 廖銘洲. "Chaotic Analysis for Nonautonomous Oscillation Circuit". Thesis, 2000. http://ndltd.ncl.edu.tw/handle/18883296270625037694.
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碩士中正理工學院
電子工程研究所
88
Recently, based on the computer technique and engineer’s research the nonlinear theory has been progressively developed. Chaos is a main topic of the nonlinear theory with the most use in research. Thus, the oscillator with trigger signal circuit, an important circuit in communication system, is presented in this paper. The frequency shift and multiple frequency oscillation usually be existed in the oscillator. It will decrease the performance of communication system. Generally, the problem is said as noise or interference. In this dissertation, we try to study in alterative points of view. In this work, the nonlinear analysis of triggered oscillation based on the two-segment criterion. We present experimental and simulated results verify the change of chaos in a non-autonomous circuits. The contribution in this dissertation are: (1) An analytical two-segment criterion is applied to the third-order non-autonomous circuits; (2) The verification of the influence of trigger signal and the phenomena of injection-lock in a oscillator circuit has been presented; (3) The implementation of chaotic circuits is available to design related chaotic circuits for practicality.
17
Yuan-chih, Chen y 陳元智. "Adaptive Sliding Control of Nonautonomous Systems". Thesis, 2001. http://ndltd.ncl.edu.tw/handle/23621126076064850932.
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碩士國立臺灣科技大學
機械工程系
89
This paper proposes a new adaptive sliding control scheme for MIMO nonlinear systems with time-varying uncertainties whose bounds are not available. The feedback linearization scheme is employed to eliminate uncertainties. Function approximators are introduced to estimate these uncertainties. Since these function approximators are realized by a finite-term orthonormal series and its coefficients are time-invariant, the update laws can be easily obtained from the Lyapunov approach to guarantee boundedness of signals and asymptotic output error convergence. On the other hand, this paper proposes an adaptive multiple-surface sliding control scheme for SISO nonlinear systems with time-varying mismatched uncertainties whose bounds are unknown. The uncertainty in subsystem is estimated by function approximation. Computer simulations and experiments are performed to show efficacy of the proposed schemes.
18
Jesus, Lopo Ferreira de. "Dynamics of nonautonomous eco-pidemiological models". Doctoral thesis, 2021. http://hdl.handle.net/10400.6/12039.
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We consider a general eco-epidemiological model which includes a large variety
of eco-epidemiological models available in the literature. We assume that the parameters
are time dependent and we consider general functions for the predation on
infected and uninfected prey and also for the vital dynamics of uninfected prey and
predator populations. We studied this model in four scenarios: non-autonomous, periodic,
discrete and random. In the non-autonomous and discrete case we discussed
the uniform strong persistence and extinction of the disease, in the periodic case, we
studied the existence of an endemic periodic orbit, and nally, in the random case
we studied the existence of random global attractors.Nesta tese consideramos um modelo eco-epidemiológico geral que inclui uma grande variedade de modelos eco-epidemiológicos presentes na literatura. Assumimos que os parâmetros dependem do tempo e consideramos funções gerais para a predação de presas infectadas e não infectadas e também para a dinâmica vital de presas não infectadas e da população de predadores. Estudamos estes modelos em quatro cenários: não-autónomo geral, periódico, discreto e aleatório. Nos casos não-autónomo geral e discreto analisamos a persistência forte e extinção da doença, no caso periódico estudamos as condições para a existência de uma órbita periódica endémica e, finalmente, no caso aleatório estudamos a existência de atratores globais aleatórios.
19
"Effective-diffusion for general nonautonomous systems". Doctoral diss., 2018. http://hdl.handle.net/2286/R.I.49071.
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abstract: The tools developed for the use of investigating dynamical systems have provided critical understanding to a wide range of physical phenomena. Here these tools are used to gain further insight into scalar transport, and how it is affected by mixing. The aim of this research is to investigate the efficiency of several different partitioning methods which demarcate flow fields into dynamically distinct regions, and the correlation of finite-time statistics from the advection-diffusion equation to these regions.
For autonomous systems, invariant manifold theory can be used to separate the system into dynamically distinct regions. Despite there being no equivalent method for nonautonomous systems, a similar analysis can be done. Systems with general time dependencies must resort to using finite-time transport barriers for partitioning; these barriers are the edges of Lagrangian coherent structures (LCS), the analog to the stable and unstable manifolds of invariant manifold theory. Using the coherent structures of a flow to analyze the statistics of trapping, flight, and residence times, the signature of anomalous diffusion are obtained.
This research also investigates the use of linear models for approximating the elements of the covariance matrix of nonlinear flows, and then applying the covariance matrix approximation over coherent regions. The first and second-order moments can be used to fully describe an ensemble evolution in linear systems, however there is no direct method for nonlinear systems. The problem is only compounded by the fact that the moments for nonlinear flows typically don't have analytic representations, therefore direct numerical simulations would be needed to obtain the moments throughout the domain. To circumvent these many computations, the nonlinear system is approximated as many linear systems for which analytic expressions for the moments exist. The parameters introduced in the linear models are obtained locally from the nonlinear deformation tensor.Dissertation/Thesis
Doctoral Dissertation Applied Mathematics 2018
20
Lai, Ting-Yu y 賴廷裕. "Codimension-Two Bifurcation in a Nonautonomous system". Thesis, 2006. http://ndltd.ncl.edu.tw/handle/71192509700646823247.
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碩士明道大學
材料暨系統工程研究所
94
Duffing equation is one of the common nonlinear differential equations with a harmonic driving force and cubic nonlinearity. The Duffing equation with hard spring, the resonance of the system is bended toward the right side. The resonance of the system is bended toward the left side and the jump phenomenon occurs in the left of the resonance in a Duffing equation with soft spring. Sometimes, the bend of the resonance may vary with the amplitude of the response. This thesis studied a novel phenomenon that the resonance of a coupled asymmetric Duffing equation with hard spring is bended toward the left side in small amplitude of the response, i.e., the dynamics of the coupled Duffing equation is similar to that of a Duffing equation with soft spring. The jump phenomenon occurs at the left side of the resonance, not at the right side. In additions, another novel co-dimension two bifurcation in a large periodic excitation. The bifurcation line constructed by the saddle-node bifurcations of period-1 tangentially intersects the bifurcation line constructed by the period doubling bifurcations of period-1. Hsiao and Tung had studied the phenomenon. Meanwhile, a Hopf bifurcation line constructed by Hopf bifurcations of period-2 merges into the co-dimension two bifurcation point and then disappears generate chaos phenomenon. This thesis studied periodic orbits of the system are detected by the shooting method. Then the stability of the periodic orbits is performed through Floquet theory. frequency responses are calculated via the harmonic balance method.
21
Tarłowski, Dawid. "Nonautonomous dynamical systems in stochastic global optimization". Praca doktorska, 2015. https://ruj.uj.edu.pl/xmlui/handle/item/45788.
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Hsiao, Yung-Chia y 蕭永嘉. "Complex Dynamics and Chaos Control of Nonautonomous systems". Thesis, 2001. http://ndltd.ncl.edu.tw/handle/02354728497908557938.
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博士國立中央大學
機械工程研究所
89
A saddle-node bifurcation with the coalescence of a stable periodic orbit and an unstable periodic orbit is a common phenomenon in nonlinear systems. This study investigates the mechanism of producing another saddle-node bifurcation with the coalescence of two unstable periodic orbits. The saddle-node bifurcation results from a codimension-two bifurcation that a period doubling bifurcation line tangentially intersects a saddle-node bifurcation line in a parameter plane. Furthermore, this thesis investigates a coalescence of the primary responses and the secondary responses in the asymmetric nonautonomous system. A subharmonic orbit that bifurcates from the primary responses coalesces with a subharmonic orbit of the secondary responses via a saddle-node bifurcation. In addition, the output of the nonautonomous system is chaotic in a specific parameter range. The chaotic motion is generally undesirable to a nonautonomous system. To control a chaotic motion to an unstable periodic orbit embedded in a chaotic trajectory, detection of the unstable periodic orbits from a chaotic time series is necessary to implement the control. This thesis presents a simple approach that detects unstable periodic orbits embedded in a chaotic motion of an unknown nonautonomous system with noisy perturbation. An identification technique is developed to obtain the model of the unknown system. The nonautonomous system is approximated by a difference system and then a global Poincaré map function is derived from the difference system. The unstable periodic orbits can be detected via the map function. The proposed method is both accurate and feasible as demonstrated by two chaotic nonautonomous systems. Many local controls of chaos were studied to suppress chaotic motions. However, there is tedious waiting time before activating the controllers. This thesis develops a strategy of controlling chaos with a region of attraction of a stabilized UPO. The strategy is activated when chaotic trajectories get into the region of attraction. The region of attraction is estimated via the approximate global Poincaré map function. The proposed strategy considerably reduces a lot of the waiting time of controlling chaos. To suppress the waiting time completely, this thesis develops a global control of chaos. The proposed global controller, who does not require waiting time in activating the controller, can be rapidly started to stabilize the targeted UPO. The global controller makes the all unstable periodic orbits vanish except a targeted unstable periodic orbit. Furthermore, a Lyapunov’s direct method is applied to confirm that the global controller can asymptotically stabilize the unique periodic orbit. Simulation results demonstrate that the global controller successfully regularizes a chaotic motion even if the chaotic trajectory is far from the targeted periodic orbit.
23
Lin, Yen-Mf y 林炎富. "Simple Stability Criterions for Second-Order Nonautonomous Systems". Thesis, 2008. http://ndltd.ncl.edu.tw/handle/09170836588790574816.
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碩士中原大學
應用數學研究所
96
A simple criterion is derived to verify the stability of second-order time-varying systems. For linear systems, we show that the exponential stability is guaranteed if the minimum amount of the damping coefficient is two times greater than the square root of the maximum stiffness. Then, the criterion is slightly extended to deal with the stabilization of a class of nonlinear nonautonomous systems. Keywords: Stability criterion, Nonautonomous systems, time-varying systems, Parametric resonance
24
李宣緯. "Studies on some nonautonomous emden-fowler differential equations". Thesis, 2010. http://ndltd.ncl.edu.tw/handle/45399483917964631311.
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Fragnelli, Genni [Verfasser]. "Delay equations with nonautonomous past / vorgelegt von Genni Fragnelli". 2002. http://d-nb.info/963845691/34.
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Chen, Jein-Shan y 陳界山. "The Almost Periodic Solutions Of The Nonautonomous Differential Equations". Thesis, 1993. http://ndltd.ncl.edu.tw/handle/55564250783476676409.
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碩士國立師範大學
數學系
81
In this paper we present some results concerned with the problem of existence of almost-periodic and asymptotically almost- solutions of non-autonomous first order abstract differential equations in Banach space. The basic techniques used are ordinary differential equation theory and fixed point theory in Banach space.
27
Rasmussen, Martin [Verfasser]. "Attractivity and bifurcation for nonautonomous dynamical systems / von Martin Rasmussen". 2006. http://d-nb.info/980394007/34.
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Shchetinina, Ekaterina [Verfasser]. "Integral manifolds for nonautonomous slow fast systems without dichotomy / von Ekaterina Shchetinina". 2004. http://d-nb.info/972647600/34.
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Chang, Yu-Hao y 張祐豪. "Cell-nonautonomous regulation of intestinal DAF-16 activities and longevity by neuronal HSF-1". Thesis, 2019. http://ndltd.ncl.edu.tw/handle/scpqra.
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Shyh, Dong Chang y 張仕東. "A Variational Approach to H**2 And H**infty Control Problems for Linear Nonautonomous System". Thesis, 1994. http://ndltd.ncl.edu.tw/handle/64623010972913767149.
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碩士國立成功大學
造船工程學系
82
In this paper, based on the variational approach, the control laws to H**2 and H**infty control problems are derived for linear time-varying systems. The variational approach allows the formulation of H**2 and H**infty - optimal control problems without the limitations placed by the orthogonality assumptions. For output feedback situation, the H**2 and H** infty - optimal state estimaters are also proposed in this reaserch through the properties of duality. The state feedback and the estimater gians are then determined by simply solving two Riccati differtial equations. Since an iteration for searching for H**infty - suboptimal control laws is needed, a computer algorithm is also attached. The theoretical developments are applied to three examples for illustrative purposes.
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Toutounji, Hazem. "Homeostatic Plasticity in Input-Driven Dynamical Systems". Doctoral thesis, 2015. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2015022613091.
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The degree by which a species can adapt to the demands of its changing environment defines how well it can exploit the resources of new ecological niches. Since the nervous system is the seat of an organism's behavior, studying adaptation starts from there. The nervous system adapts through neuronal plasticity, which may be considered as the brain's reaction to environmental perturbations. In a natural setting, these perturbations are always changing. As such, a full understanding of how the brain functions requires studying neuronal plasticity under temporally varying stimulation conditions, i.e., studying the role of plasticity in carrying out spatiotemporal computations. It is only then that we can fully benefit from the full potential of neural information processing to build powerful brain-inspired adaptive technologies. Here, we focus on homeostatic plasticity, where certain properties of the neural machinery are regulated so that they remain within a functionally and metabolically desirable range. Our main goal is to illustrate how homeostatic plasticity interacting with associative mechanisms is functionally relevant for spatiotemporal computations. The thesis consists of three studies that share two features: (1) homeostatic and synaptic plasticity act on a dynamical system such as a recurrent neural network. (2) The dynamical system is nonautonomous, that is, it is subject to temporally varying stimulation. In the first study, we develop a rigorous theory of spatiotemporal representations and computations, and the role of plasticity. Within the developed theory, we show that homeostatic plasticity increases the capacity of the network to encode spatiotemporal patterns, and that synaptic plasticity associates these patterns to network states. The second study applies the insights from the first study to the single node delay-coupled reservoir computing architecture, or DCR. The DCR's activity is sampled at several computational units. We derive a homeostatic plasticity rule acting on these units. We analytically show that the rule balances between the two necessary processes for spatiotemporal computations identified in the first study. As a result, we show that the computational power of the DCR significantly increases. The third study considers minimal neural control of robots. We show that recurrent neural control with homeostatic synaptic dynamics endows the robots with memory. We show through demonstrations that this memory is necessary for generating behaviors like obstacle-avoidance of a wheel-driven robot and stable hexapod locomotion.