On the birth of limit cycles for non-smooth dynamical systems

Abstract

The main objective of this work is to develop, via Brower degree theory and regularization theory, a variation of the classical averaging method for detecting limit cycles of certain piecewise continuous dynamical systems. In fact, overall results are presented to ensure the existence of limit cycles of such systems. These results may represent new insights in averaging, in particular its relation with non smooth dynamical systems theory. An application is presented in careful detail.

References in corpus (1)

• On three-parameter families of Filippov systems -- the fold-saddle singularity

Cited by in corpus (21)

• Averaging theory at any order for computing limit cycles of discontinuous piecewise differential systems with many zones
• Melnikov analysis in nonsmooth differential systems with nonlinear switching manifold
• Higher order Melnikov analysis for planar piecewise linear vector fields with nonlinear switching curve
• Limit cycles appearing from the perturbation of differential systems with multiple switching curves
• On the Behaviour of Under-tuned Super-Twisting Sliding Mode Control Loops
• Higher order stroboscopic averaged functions: a general relationship with Melnikov functions
• Study of periodic orbits in periodic perturbations of planar reversible Filippov systems having a two-fold cycle
• Bifurcations from families of periodic solutions in piecewise differential systems
• An averaging result for periodic solutions of Carathéodory differential equations
• Higher order analysis on the existence of periodic solutions in continuous differential equations via degree theory
• On cyclicity in discontinuous piecewise linear near-Hamiltonian differential systems with three zones having a saddle in the central one
• Periodic orbits of linear Filippov systems with a line of discontinuity
• Limit cycles of piecewise polynomial perturbations of higher dimensional linear differential systems
• On the periodic solutions of discontinuous piecewise differential systems
• Bifurcation of limit cycles from a non-smooth perturbation of a two-dimensional isochronous cylinder
• On the Hilbert number for piecewise linear vector fields with algebraic discontinuity set
• Birth of limit cycles for a class of continuous and discontinuous differential systems in (d+2)-dimension
• Limit cycles for two classes of control piecewise linear differential systems
• Invariant manifolds for piecewise smooth differential systems in ${\mathbb{R}}^3$
• Limit cycles of discontinuous piecewise quadratic and cubic polynomial perturbations of a linear center
• On the number of limit cycles for a class of discontinuous quadratic differential systems