Rich dynamics of memristor based Liénard systems

2021 ◽  
pp. 125-145
Author(s):  
S. Leo Kingston ◽  
Tomasz Kapitaniak
Keyword(s):  
Liénard Systems

scholarly journals Hopf Bifurcation of Limit Cycles in Discontinuous Liénard Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Yanqin Xiong ◽  
Maoan Han
Keyword(s):  
Hopf Bifurcation ◽  
Limit Cycles ◽  
Special Form ◽  
Bifurcation Of Limit Cycles ◽  
Liénard Systems

We consider a class of discontinuous Liénard systems and study the number of limit cycles bifurcated from the origin when parameters vary. We establish a method of studying cyclicity of the system at the origin. As an application, we discuss some discontinuous Liénard systems of special form and study the cyclicity near the origin.

scholarly journals Limit cycles in Liénard systems with saturation

2018 ◽  
Vol 51 (33) ◽  
pp. 127-131
Author(s):  
Thomas Lathuilière ◽  
Giorgio Valmorbida ◽  
Elena Panteley
Keyword(s):  
Limit Cycles ◽  
Liénard Systems

Bifurcation of Limit Cycles for Some Liénard Systems with a Nilpotent Singular Point

2015 ◽  
Vol 25 (05) ◽  
pp. 1550066 ◽  
Author(s):  
Junmin Yang ◽  
Xianbo Sun
Keyword(s):  
Singular Point ◽  
Hamiltonian Systems ◽  
Limit Cycles ◽  
Bifurcation Of Limit Cycles ◽  
Liénard Systems ◽  
Nilpotent Singular Point ◽  
Nilpotent Saddle

In this paper, we first present some general theorems on bifurcation of limit cycles in near-Hamiltonian systems with a nilpotent saddle or a nilpotent cusp. Then we apply the theorems to study the number of limit cycles for some polynomial Liénard systems with a nilpotent saddle or a nilpotent cusp, and obtain some new estimations on the number of limit cycles of these systems.

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