Complex Nonlinear Waves in Autonomous CNNs Having Two Layers of Memristor Couplings
Makoto Itoh · viXra · 2020
In this paper, we study the nonlinear waves in autonomous cellular neural networks (CNNs) having double layers of memristor coupling, by using the homotopy method. They can exhibit many interesting nonlinear waves, which are quite different from those in the single-layer autonomous CNNs. That is, the autonomous CNNs with double layers of memristor coupling can exhibit more complex nonlinear waves and more interesting bifurcation phenomena than those in the single layer autonomous CNNs. The above complex behaviors seem to be generated by the interaction with the two nonlinear waves, which are caused by the first layer and the second layer. The most remarkable point in this paper is that the autonomous CNNs with double layers can exhibit complex deformation behaviors of the nonlinear waves, due to the changes in the homotopy parameter. That is, we can generate many complex nonlinear waves by adjusting the homotopy parameter, and thereby we can control the complexity of the nonlinear waves. Furthermore, some autonomous CNNs exhibit the sensitive dependence on the homotopy parameter. That is, a small change in the homotopy parameter can result in large differences in a later state. Thus the homotopy method gives a new approach to the analysis of the complex nonlinear waves in the autonomous CNNs with double layers.