Existence and non-existence of homoclinic trajectories of the Liénard system

DOI10.3934/DCDS.1996.2.237zbMath0949.34035OpenAlexW2007552357MaRDI QIDQ1576685

Tadayuki Hara, Jitsuro Sugie

Publication date: 16 August 2000

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.1996.2.237

zbMATH Keywords

existenceperiodic solutionsLiénard systemhomoclinic trajectories

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (11)

On the homoclinic orbits of the generalized Liénard equations ⋮ THE GENERALISED LIÉNARD EQUATIONS ⋮ Unnamed Item ⋮ Limit cycles of a class of Liénard systems derived from state-dependent impulses ⋮ Nonnegativity and positivity of quadratic functionals in discrete calculus of variations: survey ⋮ Global-in-time existence of unbounded separatrices and blow-up time of solutions for Liénard systems whose restoring force is an odd power function ⋮ Conditions for approaching the origin without intersecting the x-axis in the Liénard plane ⋮ Intersection with the vertical isocline in the generalized Liénard equations ⋮ On global asymptotic stability of systems of Liénard type ⋮ Homoclinic orbits in generalized Liénard systems ⋮ Homoclinic orbits in predator-prey systems with a nonsmooth prey growth rate

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