Mathematical Physics


Nonlinear Waves in Two-Dimensional Autonomous Cellular Neural Networks Coupled by Memristors

Authors: Makoto Itoh

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 some autonomous CNNs, we have to choose a locally active memristor grid, in order for the autonomous CNNs to exhibit the continuous evolution of nonlinear waves. Some other notable features 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. 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 of this CNN. Our computer simulations show that the dynamics of the proposed autonomous CNNs are more complex than we expected.

Comments: 26 Pages.

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Submission history

[v1] 2019-12-09 22:23:41

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