Limit cycles in discontinuous classical Liénard equations

DOI10.1016/j.nonrwa.2014.04.003zbMath1301.34045OpenAlexW2062195828MaRDI QIDQ2511167

Ricardo Miranda Martins, Ana Cristina Mereu

Publication date: 5 August 2014

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2014.04.003

zbMATH Keywords

Liénard systemlimit cycleaveraging theory

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Averaging method for ordinary differential equations (34C29) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Discontinuous ordinary differential equations (34A36)

Related Items (21)

Limit cycles for perturbing Hamiltonian system inside piecewise smooth polynomial differential system ⋮ On the Number of Limit Cycles for Discontinuous Generalized Liénard Polynomial Differential Systems ⋮ Bifurcation of limit cycles by perturbing piecewise smooth integrable non-Hamiltonian systems ⋮ On the limit cycles for a class of generalized Liénard differential systems ⋮ Limit cycles in a class of switching system with a degenerate singular point ⋮ Bifurcation of limit cycles at infinity in a class of switching systems ⋮ On the limit cycles for continuous and discontinuous cubic differential systems ⋮ Bifurcations of small limit cycles in Liénard systems with cubic restoring terms ⋮ Bifurcation of Limit Cycles from a Class of Piecewise Smooth Systems with Two Vertical Straight Lines of Singularity ⋮ Nilpotent center conditions in cubic switching polynomial Liénard systems by higher-order analysis ⋮ Limit cycle bifurcations by perturbing non-smooth Hamiltonian systems with 4 switching lines via multiple parameters ⋮ Exact Solutions for the Liénard Type Model via Fractional Homotopy Methods ⋮ On the Number of Limit Cycles of Discontinuous Liénard Polynomial Differential Systems ⋮ Phase portraits of piecewise linear continuous differential systems with two zones separated by a straight line ⋮ Limit cycles bifurcating from piecewise quadratic systems separated by a straight line ⋮ Melnikov functions and limit cycles in piecewise smooth perturbations of a linear center using regularization method ⋮ A class of reversible quadratic systems with piecewise polynomial perturbations ⋮ Limit Cycles of a Class of Piecewise Smooth Liénard Systems ⋮ Hopf Bifurcation of Limit Cycles in Some Piecewise Smooth Liénard Systems ⋮ Limit cycles in piecewise polynomial systems allowing a non-regular switching boundary ⋮ A linear estimate of the number of limit cycles for some planar piecewise smooth quadratic differential system

Cites Work

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• Classical Liénard equations of degree \(n\geqslant 6\) can have \([\frac{n-1}{2}+2\) limit cycles]
• Uniqueness of limit cycles for Liénard differential equations of degree four
• Averaging methods for finding periodic orbits via Brouwer degree.
• Piecewise-smooth dynamical systems. Theory and applications
• More limit cycles than expected in Liénard equations
• Limit cycles of the generalized polynomial Liénard differential equations

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