Monotonicity of semiflows generated by cooperative delayed full-range CNNs

Abstract

The paper considers the full-range (FR) model of cellular neural networks (CNNs) with ideal hard-limiter non-linearities that limit the allowable range of the neuron state variables. It is also supposed that there is a concentrated delay (D) in the neuron interconnections. Due to the presence of multivalued nonlinearities the D-FRCNN model is mathematically described by a retarded differential inclusion. The main result is a rigorous proof that, in the case of nonsymmetric cooperative (nonnegative) interconnections, and delayed interconnections, the semiflow generated by D-FRCNNs is monotone, and that monotonicity implies some basic restrictions on the long-term behavior of the solutions. The result is compared with recent results in the literature on semiflows generated by cooperative standard CNNs, with and without delays.