Synchronization conditions in networks of Hindmarsh-Rose systems

The algebraic connectivity is crucial parameter in studying of synchronization of diffusively coupled networks. This paper studies the synchronization in networks of Hindmarsh-Rose systems, which is one of the most used neuron models. It presents sufficient condition for synchronization in these networks using the Lyapunov function method. This is a simple condition which depends on the algebraic connectivity and on the parameters of the individual system. Numerical examples are presented to illustrate the obtained results.

A Briefing Survey on Advances of Coupled Networks With Various Patterns

In real-world scenarios, networks do not exist in isolation but coupled together in different ways, including dependent, multi-support, and inter-connected patterns. And, when a coupled network suffers from structural instability or dynamic perturbations, the system with different coupling patterns shows rich phase transition behaviors. In this review, we present coupled network models with different coupling patterns developed from real scenarios in recent years for studying the system robustness. For the coupled networks with different coupling patterns, based on the network percolation theory, this paper mainly describes the influence of coupling patterns on network robustness. Moreover, for different coupling patterns, we here show readers the research background, research context, and the latest research results and applications. Furthermore, different approaches to improve system robustness with various coupling patterns and future possible research directions for coupled networks are explained and considered.

Synchronisation Conditions for a Class of Non-linearly Coupled Networks using Contraction Based Strategy

This paper describes a simple and general framework for synchronisation of non-linearly coupled dynamical systems interconnected to constitute a com- plex network. The proposed methodology of attaining synchronisation of networks is based on contraction strat- egy. The paper introduces a systematic control proce- dure to achieve synchronisation of a coupled dynamical network of proposed strict-feedback like class of nonlin- ear systems. The non-linear coupling function between different systems of the network is assumed to be in the form of bidirectional links. The proposed method- ology can be applicable to any arbitrarily structure of linear/non-linear, bidirectional or unidirectional N- coupled systems in a network. The general results have been derived for coupled systems interacting through nonlinear coupling function which are interconnected in different networked topologies including Ring, Global, Star, Arbitrary etc. The analytical conditions for syn- chronisation are expressed in terms of bounds on cou- pling strength which are derived using partial contrac- tion concepts blended with graph theory results. The proposed approach is straightforwardly applied to high dimensional non-linearly coupled chaotic systems which are common in many applications. A set of representa- tive examples of coupled chaotic systems based network are simulated to verify the theoretical results.

Reliable mode-dependent memorized projective lag synchronization for semi-Markovian jumping coupled networks

This article investigates the reliable projective lag synchronization problem for semi-Markovian jumping coupled networks under the master–slave framework. More precisely, a novel mode-dependent memorized synchronization scheme is proposed for the master and slave dynamical networks. By utilizing the Lyapunov-Krasovskii method, sufficient delay-dependent conditions are derived to achieve the reliable synchronization in the mean-square sense. Based on the derived results, the mode-dependent synchronization controller is further designed by convex optimization. In the end, two numerical examples are given to illustrate the effectiveness of the obtained theoretical results.