On the chaotic behaviour of discontinuous systems

DOI10.1007/s10884-010-9197-7zbMath1234.34029OpenAlexW2010965181MaRDI QIDQ650173

Michal Fečkan, Flaviano Battelli

Publication date: 25 November 2011

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-010-9197-7

zbMATH Keywords

bifurcationchaotic behaviourBernoulli shiftdiscontinuous systemshomoclinic cycles

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Perturbations of ordinary differential equations (34D10) Discontinuous ordinary differential equations (34A36) Complex behavior and chaotic systems of ordinary differential equations (34C28) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (15)

New global bifurcation diagrams for piecewise smooth systems: transversality of homoclinic points does not imply chaos ⋮ Chaotic threshold for non-smooth system with multiple impulse effect ⋮ Resonant periodic solutions in regularized impact oscillator ⋮ Mel'nikov methods and homoclinic orbits in discontinuous systems ⋮ On the position of chaotic trajectories ⋮ Chaos induced by sliding phenomena in Filippov systems ⋮ Subharmonic Bifurcation for a Nonsmooth Oscillator ⋮ Heteroclinic Chaotic Threshold in a Nonsmooth System with Jump Discontinuities ⋮ Threshold of Multiple Stick-Slip Chaos for an Archetypal Self-Excited SD Oscillator Driven by Moving Belt Friction ⋮ The Melnikov method for detecting chaotic dynamics in a planar hybrid piecewise-smooth system with a switching manifold ⋮ A note on invariant measures for Filippov systems ⋮ An example of chaotic behaviour in presence of a sliding homoclinic orbit ⋮ Chaos in a Periodically Perturbed Second-Order Equation with Signum Nonlinearity ⋮ Chaotic threshold of a class of hybrid piecewise-smooth system by an impulsive effect via Melnikov-type function ⋮ Bifurcations of a generalized heteroclinic loop in a planar piecewise smooth system with periodic perturbations

Cites Work

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• Bifurcations in nonlinear discontinuous systems

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