Topology and dynamics of unstable attractors

M. A. Morón; J. J. Sánchez-Gabites; J. M. R. Sanjurjo

Displaying similar documents to “Topology and dynamics of unstable attractors”

Dynamical systems and shapes.

J.J. Sánchez-Gabites (2008)

RACSAM

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This survey is an introduction to some of the methods, techniques and concepts from algebraic topology and related areas (homotopy theory, shape theory) which can be fruitfully applied to study problems concerning continuous dynamical systems. To this end two instances which exemplify the interaction between topology and dynamics are considered, namely, Conley’s index theory and the study of some properties of certain attractors.

Equivalence of ill-posed dynamical systems

Tomoharu Suda (2023)

Archivum Mathematicum

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The problem of topological classification is fundamental in the study of dynamical systems. However, when we consider systems without well-posedness, it is unclear how to generalize the notion of equivalence. For example, when a system has trajectories distinguished only by parametrization, we cannot apply the usual definition of equivalence based on the phase space, which presupposes the uniqueness of trajectories. In this study, we formulate a notion of “topological equivalence” using...

On characterization of the solution set in case of generalized semiflow

Zdeněk Beran (2009)

Kybernetika

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In the paper, a possible characterization of a chaotic behavior for the generalized semiflows in finite time is presented. As a main result, it is proven that under specific conditions there is at least one trajectory of generalized semiflow, which lies inside an arbitrary covering of the solution set. The trajectory mutually connects each subset of the covering. A connection with symbolic dynamical systems is mentioned and a possible numerical method of analysis of dynamical behavior...

Chaotic behavior and modified function projective synchronization of a simple system with one stable equilibrium

Zhouchao Wei, Zhen Wang (2013)

Kybernetika

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By introducing a feedback control to a proposed Sprott E system, an extremely complex chaotic attractor with only one stable equilibrium is derived. The system evolves into periodic and chaotic behaviors by detailed numerical as well as theoretical analysis. Analysis results show that chaos also can be generated via a period-doubling bifurcation when the system has one and only one stable equilibrium. Based on Lyapunov stability theory, the adaptive control law and the parameter update...