We study the role of network architecture in the formation of synchronous clusters in synaptically coupled networks of bursting neurons. We give a simple combinatorial algorithm that finds the largest synchronous clusters from the network topology. We demo ...
We consider dynamical systems whose parameters are switched within a discrete set of values at equal time intervals. Similar to the blinking of the eye, switching is fast and occurs stochastically and independently for different time intervals. There are t ...
Information processing with only locally connected networks such as cellular neural networks is advantageous for integrated circuit implementations. Adding long range connections can often enhance considerably their performance. It is sufficient to activat ...
We present a general framework for studying global complete synchronization in networks of dynamical systems with asymmetrical connections. We extend the connection graph stability method, originally developed for symmetrically coupled networks, to the gen ...
This paper clarifies the relation between synchronization and graph topology. Applying the Connection Graph Stability method developed by Belykh et al. [2004a] to the study of synchronization in networks of coupled oscillators, we show which graph properti ...
We study stochastically blinking dynamical systems as in the companion paper (Part I). We analyze the asymptotic properties of the blinking system as time goes to infinity. The trajectories of the averaged and blinking system cannot stick together forever, ...
We study global stability of synchronization in asymmetrically connected networks of limit-cycle or chaotic oscillators. We extend the connection graph stability method to directed graphs with node balance, the property that all nodes in the network have e ...
We propose a new model of small-world networks of cells with a time-varying coupling and study its synchronization properties. In each time interval of length /spl tau/ such a coupling is switched on with probability p and the corresponding switching rando ...
We study the influence of coupling strength and network topology on synchronization behavior in pulse-coupled networks of bursting Hindmarsh-Rose neurons. Surprisingly, we find that the stability of the completely synchronous state in such networks only de ...
We extend the connection graph stability method for complete synchronization, originally developed for symmetrically coupled networks, to the asymmetrical case. First, we study synchronization in asymmetrically connected networks with node balance, the pro ...
It is investigated to what extent the trajectories of a stochastically switched (blinking) system follow the corresponding trajectories of the averaged system. Four cases have to be distinguished, depending on whether or not the averaged system has a uniqu ...
We study the influence of coupling strength and network topology on synchronization behavior in pulse-coupled networks of bursting neurons. We find that the stability of the completely synchronous state in networks of coupled Hindmarsh-Rose neurons only de ...