Singular cycles and chaos in a new class of 3D three-zone piecewise affine systems

DOI10.1063/1.5089662zbMath1412.34151OpenAlexW2941630335WikidataQ91670329 ScholiaQ91670329MaRDI QIDQ5377545

Kai Lü, Qi-Gui Yang, Guan-Rong Chen

Publication date: 24 May 2019

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.5089662

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Qualitative investigation and simulation of ordinary differential equation models (34C60) Complex behavior and chaotic systems of ordinary differential equations (34C28) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (10)

Chaos explosion and topological horseshoe in three-dimensional impacting hybrid systems with a single impact surface ⋮ Heteroclinic Cycles Generated by Piecewise Affine Systems in ℝn ⋮ Chaos emerges from coexisting homoclinic cycles for a class of 3D piecewise systems ⋮ Special attractors and dynamic transport of the hybrid-order complex Lorenz system ⋮ Chaos Generated by a Class of 3D Three-Zone Piecewise Affine Systems with Coexisting Singular Cycles ⋮ Existence of homoclinic orbits and heteroclinic cycle in a class of three-dimensional piecewise linear systems with three switching manifolds ⋮ Heteroclinic cycles and chaos in a class of 3D three-zone piecewise affine systems ⋮ Sliding homoclinic bifurcations in a Lorenz-type system: Analytic proofs ⋮ Existence of periodic orbits and chaos in a class of three-dimensional piecewise linear systems with two virtual stable node-foci ⋮ Coexisting singular cycles in a class of three-dimensional three-zone piecewise affine systems

Cites Work

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• Chaos generator design with piecewise affine systems
• Fishing principle for homoclinic and heteroclinic trajectories
• A new method to find homoclinic and heteroclinic orbits
• The existence of Shilnikov homoclinic orbits in the Michelson system: A computer assisted proof
• Homoclinic bifurcation for a general state-dependent Kolmogorov type predator-prey model with harvesting
• A proof that the Lorenz equations have a homoclinic orbit
• On the existence of heteroclinic cycles in some class of 3-dimensional piecewise affine systems with two switching planes
• Complex dynamics in a generalized Langford system
• Including homoclinic connections and T-point heteroclinic cycles in the same global problem for a reversible family of piecewise linear systems
• The existence of homoclinic orbits in a 4D Lorenz-type hyperchaotic system
• Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system
• Homoclinic orbits and an invariant chaotic set in a new 4D piecewise affine systems
• Criteria for robustness of heteroclinic cycles in neural microcircuits
• Chaos in three-dimensional hybrid systems and design of chaos generators
• Hidden attractor and homoclinic orbit in Lorenz-like system describing convective fluid motion in rotating cavity
• Dynamics of a hyperchaotic Lorenz-type system
• Heteroclinic networks in homogeneous and heterogeneous identical cell systems
• Homoclinic and heteroclinic orbits to invariant tori in multi-degree-of-freedom Hamiltonian systems with saddle-centres
• Complex Dynamics in the Unified Lorenz-Type System
• On estimates of the bifurcation values of the parameters of a Lorentz system
• ON HOMOCLINIC AND HETEROCLINIC ORBITS OF CHEN'S SYSTEM
• HORSESHOES NEAR HOMOCLINIC ORBITS FOR PIECEWISE LINEAR DIFFERENTIAL SYSTEMS IN ℝ³
• Existence of a Reversible T-Point Heteroclinic Cycle in a Piecewise Linear Version of the Michelson System
• Dynamics at infinity and the existence of singularly degenerate heteroclinic cycles in the Lorenz system
• Existence of a Homoclinic Orbit of the Lorenz System by Precise Shooting
• Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics
• Hidden Attractors on One Path: Glukhovsky–Dolzhansky, Lorenz, and Rabinovich Systems
• Introduction to Applied Nonlinear Dynamical Systems and Chaos
• Lorenz Equations Part I: Existence and Nonexistence of Homoclinic Orbits
• The Melnikov Method and Subharmonic Orbits in a Piecewise-Smooth System
• CHAOTIFICATION OF LINEAR IMPULSIVE DIFFERENTIAL SYSTEMS WITH APPLICATIONS
• Existence of homoclinic connections in continuous piecewise linear systems

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