Homoclinic orbits in a piecewise system and their relation with invariant sets

DOI10.1016/j.physd.2003.08.002zbMath1029.37013OpenAlexW2087534361MaRDI QIDQ1413505

Rene O. Medrano-T., Iberê L. Caldas, Murilo S. Baptista

Publication date: 16 November 2003

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2003.08.002

zbMATH Keywords

stable manifoldsunstable manifoldschaotric double-scroll atractor

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items (17)

Heteroclinic cycles in a class of 3-dimensional piecewise affine systems ⋮ Theoretical and experimental time series analysis of an inductorless Chua's circuit ⋮ A new class of 3-dimensional piecewise affine systems with homoclinic orbits ⋮ Construction of a Class of Four-Dimensional Piecewise Affine Systems with Homoclinic Orbits ⋮ Horseshoes in 4-dimensional piecewise affine systems with bifocal heteroclinic cycles ⋮ The Negative Side of Chua's Circuit Parameter Space: Stability Analysis, Period-Adding, Basin of Attraction Metamorphoses, and Experimental Investigation ⋮ On the existence of homoclinic orbits in \(n\)-dimensional piecewise affine systems ⋮ Basic structures of the Shilnikov homoclinic bifurcation scenario ⋮ Shilnikov homoclinic orbit bifurcations in the Chua’s circuit ⋮ On the existence of homoclinic orbits in some class of three-dimensional piecewise affine systems ⋮ Derivation of a continuous time dynamic planar system with two unstable foci from a three-dimensional chaotic piecewise linear system ⋮ Soliton parameters and chaotic sets ⋮ Homoclinic bifurcations in reversible Hamiltonian systems ⋮ Numerical computation of connecting orbits in planar piecewise smooth dynamical system ⋮ Singular cycles connecting saddle periodic orbit and saddle equilibrium in piecewise smooth systems ⋮ Existence of homoclinic orbits and heteroclinic cycle in a class of three-dimensional piecewise linear systems with three switching manifolds ⋮ BIFURCATION IN A PIECEWISE LINEAR CIRCUIT WITH SWITCHING BOUNDARIES

Cites Work

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• Preturbulence: A regime observed in a fluid flow model of Lorenz
• The double scroll
• GLOBAL BIFURCATION ANALYSIS OF THE DOUBLE SCROLL CIRCUIT
• ON THE GENERATION OF A PERIODIC MOTION FROM TRAJECTORIES DOUBLY ASYMPTOTIC TO AN EQUILIBRIUM STATE OF SADDLE TYPE
• Differentiable dynamical systems
• A CONTRIBUTION TO THE PROBLEM OF THE STRUCTURE OF AN EXTENDED NEIGHBORHOOD OF A ROUGH EQUILIBRIUM STATE OF SADDLE-FOCUS TYPE

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