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Equilibrium analysis of cellular neural networks
Full text linkCellular neural networks are dynamical systems, described by a large set of coupled nonlinear differential equations. The equilibrium point analysis is an important step for understanding the global dynamics and for providing design rules. We yield a set of sufficient conditions (and a simple algorithm for checking them) ensuring the existence of at least one stable equilibrium point. Such conditions give rise to simple constraints, that extend the class of CNN, for which the existence of a stable equilibrium point is rigorously proved. In addition, they are suitable for design and easy to check, because they are directly expressed in term of the template elements
Influence of topology on synchronization in networks of coupled Hindmarsh-Rose neurons
No full textSynchronization plays a central role in information processing in many systems. In this work, starting from a method for predicting the behavior of the synchronous state in a network of Hindmarsh-Rose neurons, the dependence of the synchronization properties of the network on the topology is show
Synchronization in random networks with given expected degree sequences
Full text linkSynchronization in random networks with given expected degree sequences is studied. We also investigate in details the synchronization in networks whose topology is described by classical random graphs, power-law random graphs and hybrid graphs when N goes to infinity. In particular, we show that random graphs almost surely synchronize. We also show that adding small number of global edges to a local graph makes the corresponding hybrid graph to synchronize
On the effects of boundary conditions on CNN dynamics: stability and instability, bifurcation processes and chaotic phenomena
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