scholarly journals Computability in planar dynamical systems

2010 ◽  
Vol 10 (4) ◽  
pp. 1295-1312 ◽  
Author(s):  
Daniel Graça ◽  
Ning Zhong
Keyword(s):  
Dynamical Systems ◽  
Planar Dynamical Systems

BIFURCATIONS OF LIMIT CYCLES IN A Z2-EQUIVARIANT PLANAR POLYNOMIAL VECTOR FIELD OF DEGREE 7

2006 ◽  
Vol 16 (04) ◽  
pp. 925-943 ◽  
Author(s):  
JIBIN LI ◽  
MINGJI ZHANG ◽  
SHUMIN LI
Keyword(s):  
Vector Field ◽  
Dynamical Systems ◽  
Limit Cycles ◽  
Bifurcation Theory ◽  
Vector Fields ◽  
Compound Eyes ◽  
Polynomial Vector ◽  
Polynomial Vector Fields ◽  
Planar Dynamical Systems ◽  
Equivariant Vector Field

By using the bifurcation theory of planar dynamical systems and the method of detection functions, the bifurcations of limit cycles in a Z2-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 7 are studied. An example of a special Z2-equivariant vector field having 50 limit cycles with a configuration of compound eyes are given.

scholarly journals A Crossing Lemma for Annular Regions and Invariant Sets with an Application to Planar Dynamical Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Anna Pascoletti ◽  
Fabio Zanolin
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Topological Space ◽  
Fluid Mixing ◽  
Invariant Sets ◽  
Topological Horseshoes ◽  
Planar Maps ◽  
Planar Regions ◽  
Crossing Lemma ◽  
Planar Dynamical Systems

We present a topological result, namedcrossing lemma, dealing with the existence of a continuum which crosses a topological space between a pair of “opposite” sides. This topological lemma allows us to obtain some fixed point results. In the works of Pascoletti et al., 2008, and Pascoletti and Zanolin, 2010, we have widely exposed the crossing lemma for planar regions homeomorphic to a square, and we have also presented some possible applications to the theory of topological horseshoes and to the study of chaotic-like dynamics for planar maps. In this work, we move from the framework of the generalized rectangles to two other settings (annular regions and invariant sets), trying to obtain similar results. An application to a model of fluid mixing is given.

BIFURCATIONS OF LIMIT CYCLES CREATED BY A MULTIPLE NILPOTENT CRITICAL POINT OF PLANAR DYNAMICAL SYSTEMS

2011 ◽  
Vol 21 (02) ◽  
pp. 497-504 ◽  
Author(s):  
YIRONG LIU ◽  
JIBIN LI
Keyword(s):  
Dynamical Systems ◽  
Critical Point ◽  
Limit Cycles ◽  
Small Amplitude ◽  
Hopf Bifurcations ◽  
Bifurcation Phenomena ◽  
Cubic System ◽  
The Stability ◽  
Nilpotent Critical Point ◽  
Planar Dynamical Systems

Bifurcations of limit cycles created from a multiple critical point of planar dynamical systems are studied. It is different from the usual Hopf bifurcations of limit cycles created from an elementary critical point. This bifurcation phenomena depends on the stability of the multiple critical point and the multiple number of the critical point. As an example, a cubic system which can created four small amplitude limit cycles from the origin (a multiple critical point) is given.

scholarly journals Symmetry in Planar Dynamical Systems

2002 ◽  
Vol 33 (3) ◽  
pp. 357-366 ◽  
Author(s):  
N.G Lloyd ◽  
J.M Pearson
Keyword(s):  
Dynamical Systems ◽  
Planar Dynamical Systems

scholarly journals Transversally perturbed planar dynamical systems

1970 ◽  
Vol 35 (1) ◽  
pp. 187-194
Author(s):  
Roger McCann
Keyword(s):  
Dynamical Systems ◽  
Planar Dynamical Systems
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