On the critical crossing cycle bifurcation in planar Filippov systems
Reads0
Chats0
TLDR
In this paper, the authors consider planar piecewise smooth differential systems with a discontinuity line, and characterize the critical crossing cycle bifurcation, also termed as homoclinic connection to a fold.About:
This article is published in Journal of Differential Equations.The article was published on 2015-12-15 and is currently open access. It has received 41 citations till now. The article focuses on the topics: Saddle-node bifurcation & Bogdanov–Takens bifurcation.read more
Citations
More filters
Journal ArticleDOI
Discontinuity-induced limit cycles in a general planar piecewise linear system of saddle–focus type
TL;DR: In this paper, the authors dealt with the problem of limit cycles for a general planar piecewise linear differential system of saddle-focus type, using the Lienard-like canonical form with five parameters and dividing the total parameter space into several regions.
Journal ArticleDOI
A general mechanism to generate three limit cycles in planar Filippov systems with two zones
TL;DR: In this article, a general canonical form that includes all the possible configurations in planar linear systems is introduced and exploited, and the existence of a focus in one zone is sufficient to get three nested limit cycles, independently on the dynamics of the another linear zone.
Journal ArticleDOI
The pseudo-Hopf bifurcation for planar discontinuous piecewise linear differential systems
TL;DR: In this paper, the existence and uniqueness of crossing limit cycles for pseudo-Hopf bifurcation was proved under generic conditions, and a crossing limit cycle for this family was presented.
Journal ArticleDOI
Limit Cycles Induced by Threshold Nonlinearity in Planar Piecewise Linear Systems of Node-Focus or Node-Center Type
Jiafu Wang,Su He,Lihong Huang +2 more
TL;DR: This paper investigates limit cycles induced by threshold nonlinearity of piecewise linear (PWL) differential systems, which are node-focus type or node-center type with the focus or the cent...
Journal ArticleDOI
Global dynamics of a mechanical system with dry friction
TL;DR: In this article, the global dynamics of a mechanical system with dry friction was analyzed and all global phase portraits of the system were presented on the Poincare disc, which is a class of discontinuous and transcendental piecewise smooth differential systems.
References
More filters
Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
Book
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
TL;DR: In this article, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
A Reflection on Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
J. Guckenheimer,P. J. Holmes +1 more
TL;DR: In this paper, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
Book
Differential Equations with Discontinuous Righthand Sides
TL;DR: The kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics, and such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.
Book
Elements of applied bifurcation theory
TL;DR: One-Parameter Bifurcations of Equilibria in continuous-time systems and fixed points in Discrete-Time Dynamical Systems have been studied in this paper, where they have been used for topological equivalence and structural stability of dynamical systems.