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Synchronization of chaotic neural networks with delay in irregular networks. (English) Zbl 1184.34081

This paper studies the synchronization in cellular neural networks (CNNs). For the individual oscillator, the following differential delay system is taken
\[ \dot x(t)=0.001x(t)-3.8(| x_\tau +1 |-|x_\tau-1|)+ 2.85\left(\left| x_\tau+\frac{4}{3}\right| - \left| x_\tau-\frac{4}{3}\right| \right), \]
where \(x_\tau=x(t-\tau)\). Further, the authors numerically investigate different coupling combinations of five coupled oscillators with non delayed coupling. For different coupling configurations the synchronization threshold has been found, i.e. the strength of the coupling, which leads to identical synchronization of all oscillators with \(|x_i(t)-x_j(t)| \to 0\) as \(t\to\infty\) for all \(1\leq i,j\leq 5\).

MSC:

34K25 Asymptotic theory of functional-differential equations
34K23 Complex (chaotic) behavior of solutions to functional-differential equations
34K28 Numerical approximation of solutions of functional-differential equations (MSC2010)
34D06 Synchronization of solutions to ordinary differential equations
Full Text: DOI

References:

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