Controlling chaos of a dynamical system with discontinuous vector field

1997 ◽  
Vol 106 (1-2) ◽  
pp. 1-8 ◽  
Author(s):  
Haiyan Hu
Keyword(s):  
Dynamical System ◽  
Vector Field ◽  
Controlling Chaos

On Controlling Chaos in an Inflation–Unemployment Dynamical System

1999 ◽  
Vol 10 (9) ◽  
pp. 1567-1570 ◽  
Author(s):  
E. Ahmed ◽  
H ◽  
A. El-misiery ◽  
H.N. Agiza
Keyword(s):  
Dynamical System ◽  
Controlling Chaos

DYNAMICS AT INFINITY OF A CUBIC CHUA'S SYSTEM

2011 ◽  
Vol 21 (01) ◽  
pp. 333-340 ◽  
Author(s):  
MARCELO MESSIAS
Keyword(s):  
Dynamical System ◽  
Vector Field ◽  
Numerical Study ◽  
Three Dimensional ◽  
Polynomial Vector ◽  
Cubic Nonlinearity ◽  
Poincaré Compactification ◽  
Global Study ◽  
Dimensional Dynamical System ◽  
Parameter Values

We use the Poincaré compactification for a polynomial vector field in ℝ3 to study the dynamics near and at infinity of the classical Chua's system with a cubic nonlinearity. We give a complete description of the phase portrait of this system at infinity, which is identified with the sphere 𝕊2 in ℝ3 after compactification, and perform a numerical study on how the solutions reach infinity, depending on the parameter values. With this global study we intend to give a contribution in the understanding of this well known and extensively studied complex three-dimensional dynamical system.

CONTROLLING CHAOS AND THE INVERSE FROBENIUS–PERRON PROBLEM: GLOBAL STABILIZATION OF ARBITRARY INVARIANT MEASURES

2000 ◽  
Vol 10 (05) ◽  
pp. 1033-1050 ◽  
Author(s):  
ERIK M. BOLLT
Keyword(s):  
Dynamical System ◽  
Invariant Measure ◽  
Invariant Measures ◽  
Stochastic Matrix ◽  
Open Loop ◽  
Global Stabilization ◽  
Invariant Density ◽  
Controlling Chaos

The inverse Frobenius–Perron problem (IFPP) is a global open-loop strategy to control chaos. The goal of our IFPP is to design a dynamical system in ℜn which is: (1) nearby the original dynamical system, and (2) has a desired invariant density. We reduce the question of stabilizing an arbitrary invariant measure, to the question of a hyperplane intersecting a unit hyperbox; several controllability theorems follow. We present a generalization of Baker maps with an arbitrary grammar and whose FP operator is the required stochastic matrix.

Controlling Chaos with Parametric Perturbations

1998 ◽  
Vol 08 (08) ◽  
pp. 1693-1698 ◽  
Author(s):  
Leone Fronzoni ◽  
Michele Giocondo
Keyword(s):  
Dynamical System ◽  
Liquid Crystal ◽  
Dynamical Systems ◽  
Electronic Device ◽  
Parametric Perturbation ◽  
Mechanical Device ◽  
Controlling Chaos ◽  
Onset Of Chaos ◽  
Spatio Temporal ◽  
Suppression Of Chaos

We consider the effects of parametric perturbation on the onset of chaos in different dynamical systems. Favoring or suppression of chaos was observed depending on the phase or the frequency of the periodic perturbation. A lowering of the threshold of chaos was observed in an electronic device simulating a Josephson-Junction model and the suppression of chaos was obtained in a bistable mechanical device. We showed that in case of spatial instability in a sample of liquid crystal, the action of the parametric perturbation is to modify the velocity and the onset of the defects. Considering that the emergence of defects precedes the threshold of spatio-temporal chaos, we infer that parametric perturbation can modify the threshold of chaos in this spatial dynamical system.

scholarly journals Dynamical System of Gauss-Bonnet Model with Vector Field

2019 ◽  
Vol 1127 ◽  
pp. 012022
Author(s):  
Azwar Sutiono ◽  
B.J. Bansawang ◽  
Agus Suroso ◽  
Tasrief Surungan ◽  
Freddy P. Zen
Keyword(s):  
Dynamical System ◽  
Vector Field

scholarly journals STABILITY OF NEARLY-INTEGRABLE SYSTEMS WITH DISSIPATION

2013 ◽  
Vol 23 (02) ◽  
pp. 1350036 ◽  
Author(s):  
CHRISTOPH LHOTKA ◽  
ALESSANDRA CELLETTI
Keyword(s):  
Dynamical System ◽  
Vector Field ◽  
Stability Behavior ◽  
Term Stability ◽  
Long Term Stability ◽  
Nearly Integrable Systems ◽  
The Stability ◽  
Two Parameters ◽  
Action Variables

We study the stability of a vector field associated to a nearly-integrable Hamiltonian dynamical system to which a dissipation is added. Such a system is governed by two parameters, namely the perturbing and dissipative parameters, and it depends on a drift function. Assuming that the frequency of motion satisfies some resonance assumption, we investigate the stability of the dynamics, and precisely the variation of the action variables associated to the conservative model. According to the structure of the vector field, one can find linear and long-term stability times, which are established under smallness conditions of the parameters. We also provide some applications to concrete examples, which exhibit a linear or long-term stability behavior.

Suppression and Excitation of Chaos: The Example of the Glow Discharge

1998 ◽  
Vol 08 (08) ◽  
pp. 1739-1742 ◽  
Author(s):  
Thomas Braun
Keyword(s):  
Dynamical System ◽  
Glow Discharge ◽  
Numerical Simulations ◽  
Experimental Observation ◽  
Logistic Map ◽  
Dynamical Variable ◽  
Time Dependent ◽  
External Signal ◽  
Controlling Chaos ◽  
Suppression Of Chaos

I report on the experimental observation of excitation and suppression of chaos through time dependent perturbations in the dynamical variable of a glow discharge. The interaction of the external signal with the dynamical system is explained in terms of the 1D map associated to the glow discharge. Numerical simulations are also performed with the logistic map. The proposed mechanism of exciting and/or suppressing chaos is in accordance with the OGY method of controlling chaos.

CONTROLLING CHAOS IN A STATE-DEPENDENT NONLINEAR SYSTEM

2002 ◽  
Vol 12 (05) ◽  
pp. 1111-1119 ◽  
Author(s):  
TAKUJI KOUSAKA ◽  
TETSUSHI UETA ◽  
HIROSHI KAWAKAMI
Keyword(s):  
Dynamical System ◽  
Nonlinear System ◽  
Periodic Orbits ◽  
Chaotic Attractor ◽  
Discrete System ◽  
Nonlinear Dynamical System ◽  
Nonlinear Dynamical ◽  
Controlling Chaos ◽  
State Dependent ◽  
General Method

In this paper, we propose a general method for controlling chaos in a nonlinear dynamical system containing a state-dependent switch. The pole assignment for the corresponding discrete system derived from such a nonsmooth system via Poincaré mapping works effectively. As an illustrative example, we consider controlling the chaos in the Rayleigh-type oscillator with a state-dependent switch, which is changed by the hysteresis comparator. The unstable one- and two-periodic orbits in the chaotic attractor are stabilized in both numerical and experimental simulations.

Controlling chaos and response of dynamical system by synchronization

2009 ◽  
Vol 42 (3) ◽  
pp. 1466-1473 ◽  
Author(s):  
Weiyang Qin ◽  
Yongfen Yang ◽  
Zhaohui Kang ◽  
Xingmin Ren
Keyword(s):  
Dynamical System ◽  
Controlling Chaos
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