Identifiability and identification of chaotic systems based on adaptive synchronization (original) (raw)

1997, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

A New Criterion for Synchronization of Coupled Chaotic Oscillators with Application to Chua's Circuits

International Journal of Bifurcation and Chaos, 1999

A new criterion is given for choosing the coupling constant in a system of coupled chaotic oscillators to guarantee their synchronization. The criterion is derived from a new observer design methodology based on Lyapunov stability theory. As an example and application, we prove the conjecture that synchronization of two chaotic Chua circuits can be achieved with the second state as the coupling variable provided that the coupling constant is suitably chosen according to the new criterion.

A Compressed Sensing Framework of Frequency-Sparse Signals Through Chaotic System

International Journal of Bifurcation and Chaos, 2012

This paper proposes a compressed sensing (CS) framework for the acquisition and reconstruction of frequency-sparse signals with chaotic dynamical systems. The sparse signal acts as an excitation term of a discrete-time chaotic system and the compressed measurement is obtained by downsampling the system output. The reconstruction is realized through the estimation of the excitation coefficients with the principle of impulsive chaos synchronization. The l1-norm regularized nonlinear least squares is used to find the estimation. The proposed framework is easily implementable and creates secure measurements. The Hénon map is used as an example to illustrate the principle and the performance.

An Effective Synchronization Approach to Stability Analysis for Chaotic Generalized Lotka–Volterra Biological Models Using Active and Parameter Identification Methods

Entropy

In this manuscript, we systematically investigate projective difference synchronization between identical generalized Lotka–Volterra biological models of integer order using active control and parameter identification methods. We employ Lyapunov stability theory (LST) to construct the desired controllers, which ensures the global asymptotical convergence of a trajectory following synchronization errors. In addition, simulations were conducted in a MATLAB environment to illustrate the accuracy and efficiency of the proposed techniques. Exceptionally, both experimental and theoretical results are in excellent agreement. Comparative analysis between the considered strategy and previously published research findings is presented. Lastly, we describe an application of our considered combination difference synchronization in secure communication through numerical simulations.

A Fuzzy-Model-Based Chaotic Synchronization and Its Implementation on a Secure Communication System

— In this paper, a synchronization mechanism of a fuzzy-model-based chaotic system is proposed. It is then implemented on a secure communication system (SCS) for verifying its functions. The fuzzy controller is designed to guarantee master– slave synchronization to be achieved in a pre-specified convergence time. A hardware implementation with the synchronous control for the SCS is realized with a field-programmable gate array chip and a personal computer. The SCS consists of two main parts: 1) a transmitter, which contains the master system (i.e., chaotic carrier) with the input messages and 2) a receiver, which contains the slave system with the output messages. Based on the proposed synchronization method, the SCS can decrypt the output messages rapidly and correctly in the receiver in which the encrypted signals are generated by a combination of the input messages and the master system's states. It should be emphasized that since we can assign the convergence time in advance so that the user can know the suitable time for the master system to mix the input messages. Finally, the performance and merit of the proposed control scheme is exemplified by practical experiments.

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