A study on chaotic behavior in the Variable Order Fractional Liu’s System through Radial Basis Neural Networks

Abstract

Variable-order (VO) differential operators can be useful for modeling chaotical systems and non-linear fractional differential equations. In this work, we report on a study of the variable fractional (VF) domain behavior of the Liu attractor. We employ a flexible and non-linear radial basis neural network (RBNN) structure to model this complicated system. Firstly, we use a numerical scheme for the variable Order Fractional (VOF) Liu’s system in the Caputo-Fabrizio sense to calculate the physical characteristics of the complex VOF system. We investigate multiple random possibilities of control restrictions and create a parametric model using RBFNforarange of chaotic Liu’s system initial circumstances. Using the dynamical neural network structure, an investigation is conducted into the computation of several chaotic states in Liu’s system. Lyapunov exponent calculations are utilized to examine the sensitivity of chaotic behavior. The VOF Liu’s system shows succinct dynamical behavior, which makes it appropriate for dynamical system applications in real-world scenarios, as seen by phase diagrams depicting chaotic patterns. Using the average mutual information (AMI) technique, the time delay and embedding dimension of the VOF system are calculated, and the suitability of the time delay chaotic pattern in the VF domain is evaluated. At a minute time step size, these measurements are prone to variations. Our findings highlight the remarkable performance of the suggested RBFN design as a soft computing and dynamic analysis tool for chaotic systems in the VOF domain