A formal background for basic type autowaves formation by a cellular neural network

In this work, a formal background for the choice of parameters of Cellular Neural Network generating basic types of autowaves, namely, a round traveling front, a round traveling pulse and a spiral wave, is presented. This background is based on investigation of phase plane properties of a CNN cell. The required conditions for emergence of the traveling front and the traveling pulse using a one-cell initial condition are presented for two types of CNNs: with one stable node and with two stable nodes on the phase plane of a neuron pair. Simulating results are described for the round traveling front and the round traveling pulse initiated by the one-cell initial condition and for spiral waves initiated by random initial conditions