Construction of a Class of Four-Dimensional Piecewise Affine Systems with Homoclinic Orbits

DOI10.1142/S0218127416500991zbMath1343.34106OpenAlexW2465854052MaRDI QIDQ3187944

Xiao-Song Yang, Tiantian Wu

Publication date: 5 September 2016

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127416500991

zbMATH Keywords

homoclinic orbitspiecewise affine systemschaotic invariant sets

Mathematics Subject Classification ID

Discontinuous ordinary differential equations (34A36) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (5)

On the existence of homoclinic orbits in \(n\)-dimensional piecewise affine systems ⋮ Bifurcations in four-dimensional switched systems ⋮ Homoclinic orbits and an invariant chaotic set in a new 4D piecewise affine systems ⋮ Existence of periodic orbits and chaos in a class of three-dimensional piecewise linear systems with two virtual stable node-foci ⋮ Singular cycles and chaos in piecewise-affine systems

Cites Work

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• A strange attractor in the unfolding of an orbit-flip homoclinic orbit
• Homoclinic orbits and chaos in three– and four–dimensional flows
• Introduction to Applied Nonlinear Dynamical Systems and Chaos
• Existence of Chaotic Invariant Set in a Class of 4-Dimensional Piecewise Linear Dynamical Systems

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