Nonlinear Waves in Two-Dimensional Autonomous Cellular Neural Networks Coupled by Memristors
Makoto Itoh · viXra · 2019
In this paper, we propose two-dimensional autonomous cellular neural networks (CNNs), which are formed by connecting single synaptic-input CNN cells to each node of an ideal memristor grid. Our computer simulations show that the proposed two-dimensional autonomous CNNs can exhibit interesting and complex nonlinear waves. In many two-dimensional autonomous CNNs, we have to use a locally active memristor grid, in order for the autonomous CNNs to exhibit the continuous evolution of nonlinear waves. Some other notable features of the two-dimensional autonomous CNNs are: The autonomous Van der Poll type CNN can exhibit various kinds of nonlinear waves by changing the characteristic curve of the nonlinear resistor in the CNN cell. Furthermore, if we choose a different step size in the numerical integration, it exhibits a different nonlinear wave. This property is similar to the sensitive dependence on initial conditions of chaos. The autonomous Lotka-Volterra CNN can also exhibit various kinds of nonlinear waves by changing the initial conditions. That is, it can exhibit different response for each initial condition. Furthermore, we have to choose a passive memristor grid to avoid an overflow in the numerical integration process. Our computer simulations show that the dynamics of the proposed autonomous CNNs are more complex than we expected.