Adaptive Feedback Synchronization for the New Chaotic Dynamical System with Unknown Parameters

2008 ◽  
Author(s):  
Yuhua Xu ◽  
Wuneng Zhou ◽  
Hongqian Lu ◽  
Minghao Li
Keyword(s):  
Dynamical System ◽  
Unknown Parameters ◽  
Chaotic Dynamical System ◽  
Adaptive Feedback

scholarly journals Adaptive Feedback Control for Chaos Control and Synchronization for New Chaotic Dynamical System

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
M. M. El-Dessoky ◽  
M. T. Yassen
Keyword(s):  
Dynamical System ◽  
Adaptive Control ◽  
Feedback Control ◽  
Chaos Control ◽  
Control Technique ◽  
Unknown Parameters ◽  
Chaotic Dynamical System ◽  
Adaptive Feedback ◽  
Adaptive Feedback Control ◽  
Control And Synchronization

This paper investigates the problem of chaos control and synchronization for new chaotic dynamical system and proposes a simple adaptive feedback control method for chaos control and synchronization under a reasonable assumption. In comparison with previous methods, the present control technique is simple both in the form of the controller and its application. Based on Lyapunov's stability theory, adaptive control law is derived such that the trajectory of the new system with unknown parameters is globally stabilized to the origin. In addition, an adaptive control approach is proposed to make the states of two identical systems with unknown parameters asymptotically synchronized. Numerical simulations are shown to verify the analytical results.

Inverse problems for finite Jacobi matrices and Krein–Stieltjes strings

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alexander Mikhaylov ◽  
Victor Mikhaylov
Keyword(s):  
Dynamical System ◽  
Inverse Problems ◽  
Jacobi Matrix ◽  
Jacobi Matrices ◽  
Unknown Parameters ◽  
Stieltjes String ◽  
Propagation Of Waves ◽  
Dynamic Inverse

Abstract We consider dynamic inverse problems for a dynamical system associated with a finite Jacobi matrix and for a system describing propagation of waves in a finite Krein–Stieltjes string. We offer three methods of recovering unknown parameters: entries of a Jacobi matrix in the first problem and point masses and distances between them in the second, from dynamic Dirichlet-to-Neumann operators. We also answer a question on a characterization of dynamic inverse data for these two problems.

On the Potential for Entangled States Between Chaotic Systems

2014 ◽  
Vol 24 (06) ◽  
pp. 1450077 ◽  
Author(s):  
Matthew A. Morena ◽  
Kevin M. Short
Keyword(s):  
Dynamical System ◽  
Periodic Orbits ◽  
Chaotic Systems ◽  
Entangled States ◽  
Future Research ◽  
Unstable Periodic Orbits ◽  
Qualitative Information ◽  
Chaotic Dynamical System ◽  
Naturally Occurring ◽  
External Intervention

We report on the tendency of chaotic systems to be controlled onto their unstable periodic orbits in such a way that these orbits are stabilized. The resulting orbits are known as cupolets and collectively provide a rich source of qualitative information on the associated chaotic dynamical system. We show that pairs of interacting cupolets may be induced into a state of mutually sustained stabilization that requires no external intervention in order to be maintained and is thus considered bound or entangled. A number of properties of this sort of entanglement are discussed. For instance, should the interaction be disturbed, then the chaotic entanglement would be broken. Based on certain properties of chaotic systems and on examples which we present, there is further potential for chaotic entanglement to be naturally occurring. A discussion of this and of the implications of chaotic entanglement in future research investigations is also presented.

TREATMENT OF THE ERROR DUE TO UNRESOLVED SCALES IN SEQUENTIAL DATA ASSIMILATION

2011 ◽  
Vol 21 (12) ◽  
pp. 3619-3626 ◽  
Author(s):  
ALBERTO CARRASSI ◽  
STÉPHANE VANNITSEM
Keyword(s):  
Dynamical System ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Large Scale ◽  
Model Error ◽  
Environmental Modeling ◽  
Sequential Data ◽  
Chaotic Dynamical System ◽  
Error Covariance ◽  
Sequential Data Assimilation

In this paper, a method to account for model error due to unresolved scales in sequential data assimilation, is proposed. An equation for the model error covariance required in the extended Kalman filter update is derived along with an approximation suitable for application with large scale dynamics typical in environmental modeling. This approach is tested in the context of a low order chaotic dynamical system. The results show that the filter skill is significantly improved by implementing the proposed scheme for the treatment of the unresolved scales.

scholarly journals Some Chaos Notions on Dendrites

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1309
Author(s):  
Asmaa Fadel ◽  
Syahida Che Dzul-Kifli
Keyword(s):  
Dynamical System ◽  
Chaotic Dynamical System ◽  
Devaney Chaos

Transitivity is a key element in a chaotic dynamical system. In this paper, we present some relations between transitivity, stronger and alternative notions of it on compact and dendrite spaces. The relation between Auslander and Yorke chaos and Devaney chaos on dendrites is also discussed. Moreover, we prove that Devaney chaos implies strong dense periodicity on dendrites while the converse is not true.

LAG PROJECTIVE STOCHASTIC PERTURBED SYNCHRONIZATION FOR CHAOTIC SYSTEMS AND ITS APPLICATION IN SECURE COMMUNICATION

2008 ◽  
Vol 22 (24) ◽  
pp. 4175-4188 ◽  
Author(s):  
YANG TANG ◽  
JIAN-AN FANG ◽  
LIANG CHEN
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Stochastic Perturbation ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Adaptive Feedback ◽  
Communication Scheme ◽  
Simulation Results ◽  
Feedback Method

In this paper, a simple and systematic adaptive feedback method for achieving lag projective stochastic perturbed synchronization of a new four-wing chaotic system with unknown parameters is presented. Moreover, a secure communication scheme based on the adaptive feedback lag projective synchronization of the new chaotic systems with stochastic perturbation and unknown parameters is presented. The simulation results show the feasibility of the proposed method.

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