NECESSARY AND SUFFICIENT CONDITIONS OF EXISTENCE AND UNIQUENESS OF LIMIT CYCLES FOR A CLASS OF POLYNOMIAL SYSTEM

1991 ◽  
Vol 11 (1) ◽  
pp. 65-71 ◽  
Author(s):  
Deming Liu
Keyword(s):  
Limit Cycles ◽  
Existence And Uniqueness ◽  
Polynomial System ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Uniqueness Of Limit Cycles ◽  
Necessary And Sufficient

scholarly journals The non-existence, existence and uniqueness of limit cycles for quadratic polynomial differential systems

2017 ◽  
Vol 149 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Jaume Llibre ◽  
Xiang Zhang
Keyword(s):  
Differential System ◽  
Limit Cycles ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Quadratic Polynomial ◽  
Differential Systems ◽  
Polynomial Differential Systems ◽  
Polynomial Differential System ◽  
Uniqueness Of Limit Cycles

AbstractWe provide sufficient conditions for the non-existence, existence and uniqueness of limit cycles surrounding a focus of a quadratic polynomial differential system in the plane.

scholarly journals Multiple cycles and the Bautin bifurcation in the Goodwin model of a class struggle

2013 ◽  
Vol 18 (3) ◽  
pp. 265-274 ◽  
Author(s):  
Giovanni Bella
Keyword(s):  
Steady State ◽  
Limit Cycles ◽  
Sufficient Conditions ◽  
Class Struggle ◽  
Necessary And Sufficient Conditions ◽  
Goodwin Model ◽  
Multiple Cycles ◽  
Bautin Bifurcation ◽  
Necessary And Sufficient

The aim of this paper is to present the necessary and sufficient conditions for the emergence of a generalized Hopf (i.e., Bautin) bifurcation in the Goodwin’s model of a class struggle, and determine the parameter regions where multiple attracting and repelling limit cycles around the steady state may coexist.

scholarly journals Fixed point theory in the setting of $(\alpha,\beta,\psi,\phi)$-interpolative contractions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Erdal Karapınar ◽  
Andreea Fulga ◽  
Antonio Francisco Roldán López de Hierro
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Necessary And Sufficient Conditions ◽  
Alpha Beta ◽  
Necessary And Sufficient

AbstractIn this manuscript we introduce the notion of $(\alpha,\beta,\psi,\phi)$ ( α , β , ψ , ϕ ) -interpolative contraction that unifies and generalizes significant concepts: Proinov type contractions, interpolative contractions, and ample spectrum contraction. We investigate the necessary and sufficient conditions to guarantee existence and uniqueness of the fixed point of such mappings.

LIMIT CYCLES AND CENTERS IN A CUBIC PLANAR SYSTEM

2010 ◽  
Vol 20 (12) ◽  
pp. 4127-4135 ◽  
Author(s):  
LEONID CHERKAS ◽  
VALERY G. ROMANOVSKI ◽  
YEPENG XING
Keyword(s):  
Limit Cycles ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Planar System ◽  
Large Size ◽  
Necessary And Sufficient

In this paper, we obtain the necessary and sufficient conditions for centers for a cubic planar system with Z2-symmetry studied by Yu and Han [2004]. We also give an example of such a system with 12 limit cycles of "real" (relatively large) size.

Sign in / Sign up

Export Citation Format

Share Document