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In this paper, we study the dynamics of a reaction-diffusion Cellular Nonlinear Network (RD-CNN) nodel in which the reaction term is represented by Brusselator cell. We investigate the RD-CNN dynamics by means of describing function method. Comparison with classical results for Brusselator equation is provided. Then we introduce a new RD-CNN model with memristor coupling, for which the edge of chaos regime in the parameter space is determined. Numerical simulations are presented for obtaining dynamic patterns in the RD-CNN model with memristor coupling.

This paper deals with the nonlinear Schrödinger equation (NSE) with polynomial (power type) and power logarithmic nonlinearities. A third order generalization of NSE - the so called RKLE with applications in telecommunications is considered too. In some special cases the soliton solutions or the blowing up solutions can be expressed by elementary or special functions (elliptic, hyperbolic). We are looking for the wave solutions ansatz having real non-negative amplitude and linear phase. The amplitude satisfies second order nonlinear ODE and it is constructed by using the method of first integral (in mechanic processes with one degree of freedom are described by such type ODEs). So the solutions are found into integral form and one-parametric family of periodic solutions is constructed. Several illustrative examples of periodic, blowing up and soliton type solutions are proposed. [ABSTRACT FROM AUTHOR]

This paper presents a review of the theory and applications of memristor cellular nonlinear networks. By mapping the physical processes to the memristive framework, all resistive switching devices can be modeled. The idea is to find a state variable that presents with high accuracy the important features of the system, its dynamics, and time evolution in response to the inputs of the memristor. In order to develop a new design of memristor-based cellular nonlinear networks (MCNN), new circuital and mathematical memristor models need to be introduced. In this way, implementation into new software packages for computer-aided integrated circuit realization can be achieved. Another challenging problem is studying the complex behavior of MCNN models by means of local activity theory and generalizing it for various test cases. An application of the hardware implementation of these models can be found in nanostructures. [ABSTRACT FROM AUTHOR]

In this brief, a cellular neural network (CNN) vector disease model is investigated from the point of view of its dynamics. Some vector-borne diseases such as malaria, yellow fever, and typhus, which arrive and spread in new areas, are one of the main public health problems throughout the world. The investigations of the spatial spread of newly introduced diseases are interesting and challenging for both theory and applications. Existence of traveling waves for such CNN vector disease model is proved. Simulations of the obtained CNN model are given, which confirm the obtained theoretical results. Index Terms--Cellular neural network (CNN), harmonic balance method, traveling waves, vector disease model.