Poincaré maps modeling and local orbital stability analysis of discontinuous piecewise affine periodically driven systems

2007 ◽  
Vol 50 (3) ◽  
pp. 431-445 ◽  
Author(s):  
Abdelali El Aroudi ◽  
Mohamed Debbat ◽  
Luis Martinez-Salamero
Keyword(s):  
Stability Analysis ◽  
Orbital Stability ◽  
Poincaré Maps ◽  
Driven Systems ◽  
Poincare Maps ◽  
Piecewise Affine ◽  
Periodically Driven

Transport of quantum states of periodically driven systems

1990 ◽  
Vol 51 (8) ◽  
pp. 709-722 ◽  
Author(s):  
H.P. Breuer ◽  
K. Dietz ◽  
M. Holthaus
Keyword(s):  
Quantum States ◽  
Driven Systems ◽  
Periodically Driven

Noise-induced transitions between attractors in time periodically driven systems

1992 ◽  
Vol 68 (25) ◽  
pp. 3670-3673 ◽  
Author(s):  
Olaf Stiller ◽  
Andreas Becker ◽  
Lorenz Kramer
Keyword(s):  
Driven Systems ◽  
Periodically Driven

scholarly journals Effective Hamiltonians for periodically driven systems

2003 ◽  
Vol 68 (1) ◽  
Author(s):  
Saar Rahav ◽  
Ido Gilary ◽  
Shmuel Fishman
Keyword(s):  
Driven Systems ◽  
Periodically Driven ◽  
Effective Hamiltonians

Bifurcations and chaos in converters. Discontinuous vector fields and singular Poincaré maps

Nonlinearity ◽  
2000 ◽  
Vol 13 (4) ◽  
pp. 1095-1121 ◽  
Author(s):  
Gerard Olivar ◽  
Enric Fossas ◽  
Carles Batlle
Keyword(s):  
Vector Fields ◽  
Poincaré Maps ◽  
Poincare Maps ◽  
Discontinuous Vector Fields

CHAOS AND TWO-TORI IN A NEW FAMILY OF 4-CNNS

2007 ◽  
Vol 17 (03) ◽  
pp. 953-963 ◽  
Author(s):  
XIAO-SONG YANG ◽  
YAN HUANG
Keyword(s):  
Neural Networks ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Cellular Neural Networks ◽  
Lyapunov Spectrum ◽  
Regular Array ◽  
Poincaré Maps ◽  
One Dimensional ◽  
Poincare Maps ◽  
New Family

In this paper we demonstrate chaos, two-tori and limit cycles in a new family of Cellular Neural Networks which is a one-dimensional regular array of four cells. The Lyapunov spectrum is calculated in a range of parameters, the bifurcation plots are presented as well. Furthermore, we confirm the nature of limit cycle, chaos and two-tori by studying Poincaré maps.

Dynamic Analysis of a Lü Model in Six Dimensions and Its Projections

2017 ◽  
Vol 18 (5) ◽  
pp. 371-384 ◽  
Author(s):  
Luis Alberto Quezada-Téllez ◽  
Salvador Carrillo-Moreno ◽  
Oscar Rosas-Jaimes ◽  
José Job Flores-Godoy ◽  
Guillermo Fernández-Anaya
Keyword(s):  
Dynamic Analysis ◽  
Complex Variables ◽  
Bifurcation Diagrams ◽  
Poincaré Maps ◽  
Five Dimensions ◽  
Strange Nonchaotic Attractor ◽  
The Real ◽  
Poincare Maps ◽  
Extended Complex ◽  
Six Dimensions

AbstractIn this article, extended complex Lü models (ECLMs) are proposed. They are obtained by substituting the real variables of the classical Lü model by complex variables. These projections, spanning from five dimensions (5D) and six dimensions (6D), are studied in their dynamics, which include phase spaces, calculations of eigenvalues and Lyapunov’s exponents, Poincaré maps, bifurcation diagrams, and related analyses. It is shown that in the case of a 5D extension, we have obtained chaotic trajectories; meanwhile the 6D extension shows quasiperiodic and hyperchaotic behaviors and it exhibits strange nonchaotic attractor (SNA) features.

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