Homoclinical structure of the chaotic attractor

Date

2010-04-01

Author

Akhmet, Marat

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In the reference [Akhmet MU. Devaney chaos of a relay system. Commun Nonlinear Sci Numer Simulat 2009:14:1486-93.], a relay system was introduced, which admits a chaotic attractor with Devaney's ingredients. Now, we prove that the attractor consists of homo-clinic solutions. A simulation of the attractor is provided for a pendulum equation. Similar results for impulsive differential equations were announced in the plenary talk [Akhmet MU. Hyperbolic sets of impact systems. Dyn Contin Discrete Impuls Syst Set A Math Anal 2008:15(Suppl. S1):1-2. Proceedings of the 5th international conference on impulsive and hybrid dynamical systems and applications, Beijin: Watan Press: 2008.].

Subject Keywords

Relay differential equations, Hyperbolic sets, Homoclinic solutions, Heteroclinic solutions

URI

https://hdl.handle.net/11511/48504

Journal

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION

DOI

https://doi.org/10.1016/j.cnsns.2009.05.042

Collections

Department of Mathematics, Article

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Citation Formats

M. Akhmet, “Homoclinical structure of the chaotic attractor,” COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, pp. 819–822, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48504.