Dynamic Analysis of Non-linear Fractional hyperchaotic Chen System With Variable Order Utilizing RBF Network

Abstract

This research explores hyperchaotic Chen attractors in variable order fractional (VOF) dynamics, employing an innovative approach with a nonlinear and adaptive radial basis function network (RBFN). The study is initiated by computing the solutions of VOF differential equations of the hyperchaotic Chen system (H.C.S) through a numerical method in the Caputo-Fabrizio derivative, integrating variable orders across a spectrum of different system control parameters. Afterward, a comprehensive parametric model is formulated utilizing RBFN, considering various initial values of the system. In investigating the H.C.S, various chaotic and hyperchaotic features are systematically examined through a proposed simulation model incorporating varying fractional order functions. The main purpose of this study is to thoroughly analyze the sensitivity exhibited by hyperchaotic behavior, achieved by calculating Lyapunov Exponents (LE). To validate the effectiveness of the proposed computational RBFNN model, performance validation is conducted using the RMSE statistic. Significantly, the obtained outcomes closely align with those derived from numerical algorithms, emphasizing the high precision and reliability of the designed network. The outcomes of this study hold consequences for applications involving dynamic systems and hyperchaotic behavior across various scientific and engineering domains, highlighting the significance of this research in advancing the understanding and applications of variable order fractional dynamics