INTERTWINED BASINS OF ATTRACTION IN PLANAR SYSTEMS

2009 ◽  
Vol 19 (07) ◽  
pp. 2377-2381 ◽  
Author(s):  
CHANGMING DING
Keyword(s):  
Dynamical Systems ◽  
Basins Of Attraction ◽  
General Definition ◽  
Easy Condition ◽  
Planar Systems ◽  
Planar Dynamical Systems

In this paper, we investigate the intertwined basins of attraction. Using a general definition, we discuss the local intertwining properties and present an easy condition to guarantee the existence of intertwined basins for planar dynamical systems.

INTERTWINED BASINS OF ATTRACTION

2012 ◽  
Vol 22 (06) ◽  
pp. 1250130
Author(s):  
CHANGMING DING
Keyword(s):  
Dynamical Systems ◽  
Metric Space ◽  
Basins Of Attraction ◽  
General Definition ◽  
Sufficient Condition ◽  
Topological Equivalence ◽  
Definition Of

This paper deals with intertwined basins of attraction for dynamical systems in a metric space. After giving a general definition of intertwining property, which is preserved by a topological equivalence between dynamical systems, we present a sufficient condition to guarantee the existence of intertwined basins for dynamical systems in ℝn.

Revealing compactness of basins of attraction of multi-DoF dynamical systems

2018 ◽  
Vol 111 ◽  
pp. 348-361 ◽  
Author(s):  
P. Brzeski ◽  
P. Belardinelli ◽  
S. Lenci ◽  
P. Perlikowski
Keyword(s):  
Dynamical Systems ◽  
Basins Of Attraction

scholarly journals Fixed Points, Symmetries, and Bounds for Basins of Attraction of Complex Trigonometric Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Kasey Bray ◽  
Jerry Dwyer ◽  
Roger W. Barnard ◽  
G. Brock Williams
Keyword(s):  
Dynamical Systems ◽  
Fixed Points ◽  
Basins Of Attraction ◽  
Trigonometric Functions ◽  
Fractal Image ◽  
Fractal Images

The dynamical systems of trigonometric functions are explored, with a focus on tz=tanz and the fractal image created by iterating the Newton map, Ftz, of  tz. The basins of attraction created from iterating  Ftz are analyzed, and some bounds are determined for the primary basins of attraction. We further prove x- and y-axis symmetry of the Newton map and explore the nature of the fractal images.

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.

Basins of attraction in driven dynamical systems

1989 ◽  
Vol 39 (5) ◽  
pp. 2609-2627 ◽  
Author(s):  
E. Eschenazi ◽  
H. G. Solari ◽  
R. Gilmore
Keyword(s):  
Dynamical Systems ◽  
Basins Of Attraction
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