Coexisting singular cycles in a class of three-dimensional three-zone piecewise affine systems
type: Item
instance of: scholarly article
title: Coexisting singular cycles in a class of three-dimensional three-zone piecewise affine systems
author: Wenjing Xu
author: Kai Lu
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2022-09-30T00:00:00Z
review text: This paper is concerned with the dynamics for a class of three-dimensional three-zone piecewise affine systems consisting of three sub-systems, one has a real eigenvalue and a pair of complex conjugate eigenvalues. The authors study the dynamics along the unstable and stable manifolds and prove that there exist three different types of coexisting singular cycles including homoclinic and homoclinic cycles, heteroclinic and heteroclinic cycles, homoclinic and heteroclinic cycles. Moreover, they obtain some sufficient conditions for chaotic invariant sets arising from these coexisting cycles.
reviewed by: Kuilin Wu
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 34C45
zbMATH DE Number: 7595644
zbMATH Keywords: coexisting singular cycles
zbMATH Keywords: chaos
zbMATH Keywords: piecewise affine system
zbMATH Keywords: switching manifold
zbMATH Keywords: complex dynamics
MaRDI profile type: Publication
full work available at URL: dcdsb.2022045
OpenAlex ID: W4226395615
cites work: A new method to find homoclinic and heteroclinic orbits
cites work: Generating Shilnikov chaos in 3D piecewise linear systems
cites work: Q3697395
cites work: A Lorenz-type attractor in a piecewise-smooth system: Rigorous results
cites work: Sliding homoclinic bifurcations in a Lorenz-type system: Analytic proofs
cites work: Piecewise-smooth dynamical systems. Theory and applications
cites work: Including homoclinic connections and T-point heteroclinic cycles in the same global problem for a reversible family of piecewise linear systems
cites work: Existence of homoclinic connections in continuous piecewise linear systems
cites work: Existence of a Reversible T-Point Heteroclinic Cycle in a Piecewise Linear Version of the Michelson System
cites work: The existence of homoclinic orbits in a 4D Lorenz-type hyperchaotic system
cites work: A new Lorenz-type hyperchaotic system with a curve of equilibria
cites work: Heteroclinic Cycles in a Competitive Network
cites work: Canonical piecewise-linear analysis
cites work: Rigorous verification of cocoon bifurcations in the Michelson system
cites work: Dynamics and bifurcations of non-smooth mechanical systems
cites work: On estimates of the bifurcation values of the parameters of a Lorentz system
cites work: General existence conditions of homoclinic trajectories in dissipative systems. Lorenz, Shimizu-Morioka, Lu and Chen systems
cites work: Hidden attractor and homoclinic orbit in Lorenz-like system describing convective fluid motion in rotating cavity
cites work: Homoclinic Bifurcations and Chaos in the Fishing Principle for the Lorenz-like Systems
cites work: Dynamics of a new Lorenz-like chaotic system
cites work: Identification of piecewise linear dynamical systems using physically-interpretable neural-fuzzy networks: methods and applications to origami structures
cites work: HORSESHOES NEAR HOMOCLINIC ORBITS FOR PIECEWISE LINEAR DIFFERENTIAL SYSTEMS IN ℝ3
cites work: Deterministic Nonperiodic Flow
cites work: Chaos Generated by a Class of 3D Three-Zone Piecewise Affine Systems with Coexisting Singular Cycles
cites work: Singular cycles and chaos in a new class of 3D three-zone piecewise affine systems
cites work: Heteroclinic cycles and chaos in a class of 3D three-zone piecewise affine systems
cites work: Strange attractors and wandering domains near a homoclinic cycle to a bifocus
cites work: Q4947577
cites work: Scenario of the Birth of Hidden Attractors in the Chua Circuit
cites work: Heteroclinic cycles in a class of 3-dimensional piecewise affine systems
cites work: Existence of Homoclinic Cycles and Periodic Orbits in a Class of Three-Dimensional Piecewise Affine Systems
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cites work: Homoclinic orbits and an invariant chaotic set in a new 4D piecewise affine systems
cites work: Complex dynamics in a generalized Langford system
cites work: Homoclinic orbits and chaos in the generalized Lorenz system
DOI: 10.3934/DCDSB.2022045
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description: scientific article; zbMATH DE number 7595644