Mel'nikov methods and homoclinic orbits in discontinuous systems

DOI10.1007/s10884-013-9307-4zbMath1285.34040OpenAlexW2017670277MaRDI QIDQ376312

Alessandro Calamai, Matteo Franca

Publication date: 4 November 2013

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

Full work available at URL: https://doi.org/10.1007/s10884-013-9307-4

zbMATH Keywords

homoclinic solutionsdiscontinuous systemsMel'nikov integrals

Mathematics Subject Classification ID

Discontinuous ordinary differential equations (34A36) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) 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 ⋮ Melnikov Theory for Two-Dimensional Manifolds in Three-Dimensional Flows ⋮ Heteroclinic bifurcation in a class of planar piecewise smooth systems with multiple zones ⋮ On the existence of homoclinic orbits in \(n\)-dimensional piecewise affine systems ⋮ On the position of chaotic trajectories ⋮ Impulsive perturbations to differential equations: stable/unstable pseudo-manifolds, heteroclinic connections, and flux ⋮ On the robustness property of nonuniform exponential dichotomies ⋮ Melnikov theory for nonlinear implicit ODEs ⋮ Melnikov theory for weakly coupled nonlinear RLC circuits ⋮ The Melnikov method for detecting chaotic dynamics in a planar hybrid piecewise-smooth system with a switching manifold ⋮ Structure results for semilinear elliptic equations with Hardy potentials ⋮ Entire solutions of superlinear problems with indefinite weights and Hardy potentials ⋮ Discontinuity-induced limit cycles in a general planar piecewise linear system of saddle-focus type ⋮ Melnikov Method for a Class of Planar Hybrid Piecewise-Smooth Systems ⋮ General Melnikov approach to implicit ODE's

Cites Work

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• Exponential dichotomies, heteroclinic orbits, and Melnikov functions
• Melnikov method for discontinuous planar systems
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• Nonsmooth impact mechanics. Models, dynamics and control
• HORSESHOES NEAR HOMOCLINIC ORBITS FOR PIECEWISE LINEAR DIFFERENTIAL SYSTEMS IN ℝ³
• The double scroll family
• One-Parameter Bifurcations in Planar Filippov Systems
• Bifurcations in nonlinear discontinuous systems
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