Periodic sinks and periodic saddle orbits induced by heteroclinic bifurcation in three-dimensional piecewise linear systems with two zones

DOI10.1016/j.amc.2021.126200OpenAlexW3148932784MaRDI QIDQ2243197

Lei Wang, Xiao-Song Yang, Qingdu Li

Publication date: 11 November 2021

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2021.126200

zbMATH Keywords

stabilityperiodic orbitsbifurcationpiecewise linear systemsheteroclinic loopsperiodic saddle orbitsperiodic sinks

Mathematics Subject Classification ID

Qualitative theory for ordinary differential equations (34Cxx) Nonlinear dynamics in mechanics (70Kxx) Local and nonlocal bifurcation theory for dynamical systems (37Gxx)

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Dynamical analysis in a piecewise smooth predator–prey model with predator harvesting ⋮ Global-in-time existence of unbounded separatrices and blow-up time of solutions for Liénard systems whose restoring force is an odd power function ⋮ Bifurcation of periodic orbits and its application for high-dimensional piecewise smooth near integrable systems with two switching manifolds

Cites Work

• Unnamed Item
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• Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth differential systems
• Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system with a homoclinic loop
• Periodic orbits and invariant cones in three-dimensional piecewise linear systems
• Fundamental matrix solutions of piecewise smooth differential systems
• Generalized Hopf bifurcation for planar Filippov systems continuous at the origin
• Jumps of the fundamental solution matrix in discontinuous systems and applications
• On Hopf bifurcation in non-smooth planar systems
• Global bifurcations and chaos. Analytical methods
• Existence of piecewise linear differential systems with exactly \(n\) limit cycles for all \(n\in \mathbb N\)
• The existence and stability analyses of periodic orbits in 3-dimensional piecewise affine systems
• On the applicability of the approximate Poincaré mapping to the analysis of dynamics induced by ODE systems. I: Proximity of mappings
• On the applicability of the approximate Poincaré mapping to the analysis of dynamics induced by ODE systems. II: Proximity of coordinate partial derivatives of Poincaré mappings
• Chaos in three-dimensional hybrid systems and design of chaos generators
• On the number of limit cycles in general planar piecewise linear systems of node-node types
• Analytical search for homoclinic bifurcations in the Shimizu-Morioka model
• Piecewise-smooth dynamical systems. Theory and applications
• Heteroclinic cycles in a class of 3-dimensional piecewise affine systems
• General existence conditions of homoclinic trajectories in dissipative systems. Lorenz, Shimizu-Morioka, Lu and Chen systems
• Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth systems with a cusp
• On the existence and uniqueness of limit cycles in planar continuous piecewise linear systems without symmetry
• Existence of periodic orbits in grazing bifurcations of impacting mechanical oscillators
• Planar systems of piecewise linear differential equations with a line of discontinuity
• Generalized Hopf bifurcation in a class of planar switched systems
• FOLLOWING A SADDLE-NODE OF PERIODIC ORBITS' BIFURCATION CURVE IN CHUA'S CIRCUIT
• Energy Pumping in Nonlinear Mechanical Oscillators: Part I—Dynamics of the Underlying Hamiltonian Systems
• A BIPARAMETRIC BIFURCATION IN 3D CONTINUOUS PIECEWISE LINEAR SYSTEMS WITH TWO ZONES: APPLICATION TO CHUA'S CIRCUIT
• On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities
• Existence of a Reversible T-Point Heteroclinic Cycle in a Piecewise Linear Version of the Michelson System
• Generalized Hopf bifurcation for non-smooth planar systems
• Centennial History of Hilbert's 16th Problem
• Chaotic Dynamics in Four-Dimensional Piecewise Affine Systems with Bifocal Heteroclinic Cycles
• Existence of Homoclinic Cycles and Periodic Orbits in a Class of Three-Dimensional Piecewise Affine Systems
• One-Parameter Bifurcations in Planar Filippov Systems
• Introduction to Applied Nonlinear Dynamical Systems and Chaos
• Existence of homoclinic connections in continuous piecewise linear systems
• Canonical Discontinuous Planar Piecewise Linear Systems
• LIMIT CYCLE BIFURCATION IN 3D CONTINUOUS PIECEWISE LINEAR SYSTEMS WITH TWO ZONES: APPLICATION TO CHUA'S CIRCUIT
• Existence of Chaotic Invariant Set in a Class of 4-Dimensional Piecewise Linear Dynamical Systems

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