BOUALLEGUE EQUATION SYSTEM AND ITS APPLICATIONS IN CHAOS THEORY

This paper presents a new contribution in chaos theory using Bouallegue Equation System, this system is built of three blocks, These blocks are connected in cascade, the first block is a system of chaotic attractor,the second block is a system of fractal processes and the third block is a system of neural networks. In this work, we have generated a novel class of hyper chaotic attractors by coupling with neuron containing multi dendrites, each dendrite has its activation function. The activation function contains four parameters form,position of dendrite, parameter of equilibrium and polarity. Each dendrite can take four behaviors by configuration the parameter n, its structure contains four variables (n, p, q, x), so we call this capacity or this potential of activation function, a Variable Structure Model of Neuron (VSMN, for short). The impact of activation function in chaotic attractor generates a new classes of hyper chaos attractors with fluctuation, cutting, folding, amplifying in attractors. Simulations have demonstrated the validity and feasibility of the proposed method. Two results of applications using Bouallegue Equation System in fractal theory are also given to show the similarities in medicine illustrating the fractal chromosome and the fractal lung, and in biology displaying a fractal flower. Copyright (C) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)