Global exponential stability of cellular neural networks with multi-proportional delays

In this paper, a class of cellular neural networks (CNNs) with multi-proportional delays is studied. The nonlinear transformation yi(t) = xi(et) transforms a class of CNNs with multi-proportional delays into a class of CNNs with multi-constant delays and time-varying coefficients. By applying Brouwer fixed point theorem and constructing the delay differential inequality, several delay-independent and delay-dependent sufficient conditions are derived for ensuring the existence, uniqueness and global exponential stability of equilibrium of the system and the exponentially convergent rate is estimated. And several examples and their simulations are given to illustrate the effectiveness of obtained results.

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