Propagation phenomena for CNNs with asymmetric templates and distributed delays
This work considers a Cellular Neural Network modeled by a sequence of nodes, each of which has a voltage varying in time according to the interaction with the neighbors (up to a certain level). Such an interaction, described by a nonlinear term, can be asymmetric and exhibits distributed time delay. When the nonlinearity is nondecreasing, the theory of monotone dynamical systems is applied to prove the existence and some estimates of asymptotic speed of spread, both to the left and to the right. When the nonlinearity is not monotone, instead, the same results are obtained by comparing the original system with two monotone ones and using the previous part. In addition, the authors show that the spreading speed coincides with the minimal speed of traveling waves. Finally, some numerical experiments are presented.
scientific article; zbMATH DE number 6806973
scientific article