Journal Article

·2018

The vector‐matrix form numerical simulations for time‐derivative cellular neural networks

Sadiye Nergis Tural-Polat YTU

International Journal of Numerical Modelling Electronic Networks Devices and Fields

Abstract

Abstract Time‐derivative cellular neural network (TDCNN) state equations can be written in vector‐matrix form which enables the application of discrete‐time numerical simulation methods. In this paper, existing numerical simulation methods are adapted for TDCNN for the first time, namely, MATLAB ordinary differential equation simulation and the vector‐matrix fourth‐order Runge‐Kutta approximation. Afterwards, several simulation methods for TDCNN are analyzed. The ordinary differential equation solvers in MATLAB program, fourth‐order Runge‐Kutta approximation, and the forward Euler approximation are used in the numerical simulation of the vector‐matrix form TDCNN. Our previously proposed fast simulation method for TDCNNs is revisited. The methods are discussed from a programmer's point of view, and the results are presented.

Keywords

Euler method Runge–Kutta methods Matrix (chemical analysis) Ordinary differential equation Applied mathematics MATLAB Computer science Computer simulation Differential equation Artificial neural network State vector State-transition matrix Euler's formula Mathematics Algorithm Mathematical analysis Symmetric matrix Physics Classical mechanics Simulation Artificial intelligence

Subject Areas

Neural Networks Stability and Synchronization ·Computer Networks and Communications ·Physical Sciences
Cellular Automata and Applications ·Computational Theory and Mathematics ·Physical Sciences
Neural Networks and Applications ·Artificial Intelligence ·Physical Sciences

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