Giuseppe Grassi

Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal

In this work control theory is used to formalize hyperchaos synchronization as a nonlinear observer design issue. Following this approach, a new systematic tool to synchronize a class of hyperchaotic systems via a scalar transmitted signal is developed. The proposed technique has been applied to synchronize two well-known hyperchaotic systems.

NEW 3D-SCROLL ATTRACTORS IN HYPERCHAOTIC CHUA'S CIRCUITS FORMING A RING

This paper presents an approach for generating new hyperchaotic attractors in a ring of Chuas circuits. By taking a closed chain of three circuits and exploiting sine functions as nonlinearities, the proposed technique enables 3D-scroll attractors to be generated. In particular, the paper shows that 3D-scroll dynamics can be designed by modifying six parameters related to the circuit nonlinearities.

A system theory approach for designing cryptosystems based on hyperchaos

In this paper a general methodology for designing chaotic and hyperchaotic cryptosystems is developed. The basic idea is to make the decrypter a nonlinear observer for the state of the encrypter. Referring to this concept, some propositions are given which enable the plaintext to be retrieved if proper structural properties of the chaotic system hold. The proposed tool proves to be powerful and flexible, since a wide class of cryptosystems can be designed by exploiting different chaotic and hyperchaotic circuits. The advantages of the suggested approach are illustrated in detail. In particular, the utilization of hyperchaos-based cryptosystems, as well as the increased complexity of the transmitted signal, make a contribution to the development of communication systems with higher security.

Theory and experimental realization of observer-based discrete-time hyperchaos synchronization

Research in the synchronization of dynamical systems has been mainly focused on chaotic rather than hyperchaotic systems and on continuous-time rather than discrete-time systems. Numerical simulations dominate these studies and results typically lack experimental data. This brief fills these gaps by 1) presenting a technique for the exact (dead-beat) synchronization of hyperchaotic discrete-time systems; and 2) describing an electronic implementation of this technique for the generalized Henon map. The synchronization strategy is based on the observer concept and enables a wide class of hyperchaotic discrete-time systems to be synchronized via a scalar signal. An electronic implementation provides verification of the theoretical results and confirms the feasibility of realizing this approach in hardware.

A new approach to design cellular neural networks for associative memories

In this brief, a synthesis procedure of cellular neural networks for associative memories is presented, The proposed method, by assuring the global asymptotic stability of the equilibrium point, generates networks where the input data are fed via external inputs rather than initial conditions. This new approach enables to design both heteroassociative and autoassociative memories and reveals particularly suitable for VLSI implementation techniques.

CONTROLLING CHAOTIC DYNAMICS USING BACKSTEPPING DESIGN WITH APPLICATION TO THE LORENZ SYSTEM AND CHUA'S CIRCUIT

In this Letter backstepping design is proposed for controlling chaotic systems. The tool consists in a recursive procedure that combines the choice of a Lyapunov function with the design of feedback control. The advantages of the method are the following: (i) it represents a systematic procedure for controlling chaotic or hyperchaotic dynamics; (ii) it can be applied to several circuits and systems reported in literature; (iii) stabilization of chaotic motion to a steady state as well as tracking of any desired trajectory can be achieved. In order to illustrate the general applicability of backstepping design, the tool is utilized for controlling the chaotic dynamics of the Lorenz system and Chuas circuit. Finally, numerical simulations are carried out to show the effectiveness of the technique.

On discrete-time cellular neural networks for associative memories

In this paper, discrete-time cellular neural networks (DTCNNs) with a globally asymptotically stable equilibrium point, are designed to behave as associative memories. The objective is achieved by considering feedback parameters related to circulant matrices and by satisfying frequency domain stability criteria. The approach, by generating DTCNNs where the input data are fed via external inputs rather than initial conditions, enables both heteroassociative and autoassociative memories to be designed. Numerical examples are reported in order to show the capabilities of the proposed tool.

Experimental realization of observer-based hyperchaos synchronization

Research literature on the topic of synchronizing hyperchaotic systems predominantly addresses theoretical issues-most investigations lack experimental results. This paper aims to bridge this gap by presenting an electronic circuit implementation of a particular hyperchaotic synchronization strategy. Specifically, previous research has demonstrated that linear observers may be synchronized to a certain class of hyperchaotic systems via a scalar signal. This paper describes an experimental realization of this type of linear observer for the four-dimensional hyperchaotic system proposed by Tamasevicius et al. For comparative purposes, the linear observer circuitry may be electronically reconfigured as a second resistively coupled hyperchaotic oscillator. Experimental results, provided for both cases, verify theoretical results, demonstrate the feasibility of electronically implementing linear observers for hyperchaotic oscillators, and suggest that the linear observer is robust with respect to component mismatches between the hyperchaotic oscillator and the linear observer.

Hyperchaotic Coupled Chua Circuits: An Approach for Generating New n×m-Scroll Attractors

In this paper an approach for generating new hyperchaotic attractors from coupled Chua circuits is proposed. The technique, which exploits sine functions as nonlinearities, enables n×m-scroll attractors to be generated. In particular, it is shown that n×m-scroll dynamics can be easily designed by modifying four parameters related to the circuit nonlinearities. Simulation results are reported to illustrate the capability of the proposed approach.

FRACTIONAL-ORDER CHUA'S CIRCUIT: TIME-DOMAIN ANALYSIS, BIFURCATION, CHAOTIC BEHAVIOR AND TEST FOR CHAOS

In this tutorial the chaotic behavior of the fractional-order Chuas circuit is investigated from the time-domain point of view. The objective is achieved using the Adomian decomposition method, wh...