Chaos in singular impulsive O.D.E.

DOI10.1016/0362-546X(95)00182-UzbMath0919.34016MaRDI QIDQ5689167

Michal Fečkan, Flaviano Battelli

Publication date: 20 February 1997

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

Melnikov functionsLyapunov-Schmidt proceduretransversal homoclinic orbits

Mathematics Subject Classification ID

Ordinary differential equations with impulses (34A37) Complex behavior and chaotic systems of ordinary differential equations (34C28) Singular perturbations for ordinary differential equations (34E15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items

Chaotic threshold for a class of impulsive differential system ⋮ Chaotification of Impulsive Systems by Perturbations ⋮ Chaotic threshold for non-smooth system with multiple impulse effect ⋮ Existence of nontrivial weak homoclinic orbits for second-order impulsive differential equations ⋮ Relaxed controls for nonlinear fractional impulsive evolution equations ⋮ Existence conditions for bounded solutions of weakly perturbed linear impulsive systems ⋮ COMPLEXITY OF A DELAYED PREDATOR–PREY MODEL WITH IMPULSIVE HARVEST AND HOLLING TYPE II FUNCTIONAL RESPONSE ⋮ Periodic BVPs for fractional order impulsive evolution equations

Cites Work

• On the existence of chaotic behaviour of diffeomorphisms
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• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• An example of bifurcation to homoclinic orbits
• Bifurcation of heteroclinic orbits for diffeomorphisms
• Bounded solutions to singularly perturbed systems of O. D. E
• Chaos in the Duffing equation
• Exponential dichotomies and transversal homoclinic points
• Melnikov functions for singularly perturbed ordinary differential equations
• Differentiable dynamical systems
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