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

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.

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

A Numerical Simulation of Controlling Chaotic Vibration of a Maglev System by OGY Method

2003 ◽  
Author(s):  
Zhixiang Xu ◽  
Zhengjin Feng ◽  
Kunisato Seto ◽  
Hideyuki Tamura
Keyword(s):  
Dynamical System ◽  
Numerical Simulation ◽  
Continuous Time ◽  
Controlling Chaos ◽  
Maglev System ◽  
Chaotic Vibrations ◽  
Chaotic Vibration ◽  
Model Based ◽  
Simulation Results

In this paper, we first introduced the Model-based OGY method for controlling chaos of nonlinear continuous time dynamical system, and then applied this Model-Based OGY Method to a repulsive maglev system to control its chaotic vibrations. From the numerical simulation results, we found out that the Model-based OGY Method is successfully applied to controlling chaotic vibrations of the repulsive maglev system, and hence the effectivity of Model-based OGY Method is demonstrated.

scholarly journals Locating and Stabilizing Unstable Periodic Orbits Embedded in the Horseshoe Map

2021 ◽  
Vol 31 (04) ◽  
pp. 2150110
Author(s):  
Yuu Miino ◽  
Daisuke Ito ◽  
Tetsushi Ueta ◽  
Hiroshi Kawakami
Keyword(s):  
Dynamical System ◽  
Periodic Orbits ◽  
Ad Hoc ◽  
Computation Method ◽  
Control Input ◽  
Unstable Periodic Orbits ◽  
Stable And Unstable Manifolds ◽  
Controlling Chaos ◽  
Dimensional Dynamical System ◽  
The Given

Based on the theory of symbolic dynamical systems, we propose a novel computation method to locate and stabilize the unstable periodic points (UPPs) in a two-dimensional dynamical system with a Smale horseshoe. This method directly implies a new framework for controlling chaos. By introducing the subset based correspondence between a planar dynamical system and a symbolic dynamical system, we locate regions sectioned by stable and unstable manifolds comprehensively and identify the specified region containing a UPP with the particular period. Then Newton’s method compensates the accurate location of the UPP with the regional information as an initial estimation. On the other hand, the external force control (EFC) is known as an effective method to stabilize the UPPs. By applying the EFC to the located UPPs, robust controlling chaos is realized. In this framework, we never use ad hoc approaches to find target UPPs in the given chaotic set. Moreover, the method can stabilize UPPs with the specified period regardless of the situation where the targeted chaotic set is attractive. As illustrative numerical experiments, we locate and stabilize UPPs and the corresponding unstable periodic orbits in a horseshoe structure of the Duffing equation. In spite of the strong instability of UPPs, the controlled orbit is robust and the control input retains being tiny in magnitude.

Controlling Chaos of Planar Closed Chain Underactuated Mechanism With the Edge of Chaos

2016 ◽  
Author(s):  
Jin Xie ◽  
Bichun Ren ◽  
Zhaohui Liu ◽  
Yong Chen
Keyword(s):  
Dynamical System ◽  
Time Series ◽  
Chaotic Motion ◽  
Permutation Entropy ◽  
Underactuated Mechanism ◽  
Controlling Chaos ◽  
Edge Of Chaos ◽  
Closed Chain

Under some circumstances, a planar closed chain five-bar underactuated mechanism exhibits chaotic motion. The edge of chaos is the transitory region between deterministic and chaotic motion. A new idea to control chaos by changing the parameters of the dynamical system at the edge of chaos is proposed in this paper. Permutation entropy is employed to detect the edge of chaos, and its normalizing equation is modified for making it more sensitive to the irregularity of the time series. Instead of the dynamical edge of chaos, the static edge of chaos is utilized to make the plan of controlling chaos. The study is conducted experimentally. The results show that the method proposed in this paper can control the chaos arising from the underactuated mechanism successfully.

Sign in / Sign up

Export Citation Format

Share Document