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Synchronization in an array of nonlinearly coupled chaotic neural networks with delay coupling. (English) Zbl 1165.34414
Summary: A general complex dynamical network consisting of $N$ nonlinearly coupled identical chaotic neural networks with coupling delays is firstly formulated. Many studied models with coupling systems are special cases of this model. Synchronization in such dynamical network is considered. Based on the Lyapunov--Krasovskii stability theorem, some simple controllers with updated feedback strength are introduced to make the network synchronized. The update gain $\gamma_i$ can be properly chosen to make some important nodes synchronized quicker or slower than the rest. Two examples including nearest-neighbor coupled networks and scale-free network are given to verify the validity and effectiveness of the proposed control scheme.

##### MSC:
 34K25 Asymptotic theory of functional-differential equations 34K23 Complex (chaotic) behavior of solutions of functional-differential equations 92B20 General theory of neural networks (mathematical biology)
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