Łojasiewicz inequality and exponential convergence of the full-range model of CNNs
International Journal of Circuit Theory and Applications
A study on semiflows generated by cooperative full-range CNNs
International Journal of Circuit Theory and Applications
Fast texture synthesis with cellular neural network-based patch stitching
International Journal of Circuit Theory and Applications
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This paper compares the dynamical behaviour of the standard (S) cellular neural networks (CNNs) and the full-range (FR) CNNs, when the two CNN models are characterized by the same set of parameters (interconnections and inputs). The FR-CNNs are assumed to be characterized by ideal hard-limiter nonlinearities with two vertical segments in the i–v characteristic. The main result is that some basic conditions ensuring global exponential stability (GES) of the unique equilibrium point of S-CNNs, with or without delay, continue to ensure the same property for FR-CNNs for the same set of parameters. The significance of this result is discussed with respect to the results in a paper by Corinto and Gilli addressing the similarity of the qualitative behaviour of S-CNNs and FR-CNNs. FR-CNNs are analysed in this paper from a rigorous mathematical viewpoint by means of theoretical tools from set-valued analysis and differential inclusions. In particular, GES is investigated via an extended Lyapunov approach that is applicable to the differential inclusion describing the dynamics of FR-CNNs. Copyright © 2007 John Wiley & Sons, Ltd.