Network analysis of complex biological systems : boundedness of weakly reversible chemical reaction networks and conditions for synchronisation of coupled oscillators

Imperial Users onl

Synchronization of chaotic dynamical systems: a brief review

There are several reasons for the approach to chaos synchronization. This phenomenon is immediately interesting because of its high potential for applications. But, first of all, it is particularly interesting the study of a phenomenon that requires the adjustment of dynamic behaviors in order to obtain a coincident chaotic motion, being this possible even in chaotic dynamical systems in which sensitive dependence on initial conditions is one of the features. The possibility of applying techniques of chaos control in order to optimize the results of synchronization is alsoa motivating factor for the study of this phenomenon. It is presented a brief review of preliminary notions on nonlinear dynamics and then is considered in detail the synchronization of chaotic dynamical systems, both in continuous and discrete time

Extreme multistability in a chemical model system

Coupled systems can exhibit an unusual kind of multistability, namely, the coexistence of infinitely many attractors for a given set of parameters. This extreme multistability is demonstrated to occur in coupled chemical model systems with various types of coupling. We show that the appearance of extreme multistability is associated with the emergence of a conserved quantity in the long-term limit. This conserved quantity leads to a slicing of the state space into manifolds corresponding to the value of the conserved quantity. The state space slices develop as t→∞ and there exists at least one attractor in each of them. We discuss the dependence of extreme multistability on the coupling and on the mismatch of parameters of the coupled systems

Synchronization between Bidirectional Coupled Nonautonomous Delayed Cohen-Grossberg Neural Networks

Based on using suitable Lyapunov function and the properties of M-matrix, sufficient conditions for complete synchronization of bidirectional coupled nonautonomous Cohen-Grossberg neural networks are obtained. The methods for discussing synchronization avoid complicated error system of Cohen-Grossberg neural networks. Two numerical examples are given to show the effectiveness of the proposed synchronization method

Properties of generalized synchronization of chaos

A review of recent ideas in the field of generalized synchronization of chaos is presented. This field is concerned with a generalization of the concept of conventional (identical) chaotic synchronization to the case of one-way coupled nonidentical chaotic systems. Generalized synchronization is taken to occur if, ignoring transients, the response system becomes uniquely determined by the current state of the driving system, i. e., all trajectories in the phase space are attracted to a complex synchronization manifold that may have a fractal structure. Different tools for detecting and analyzing the properties of this type of synchronization are discussed