Design of intelligent computing networks for nonlinear chaotic fractional Rossler system

Abstract

In a recent development, the legacy of fractional-order multi-dimensional chaotic systems has attracted numerous researchers owing to their valuable applications in cryptology, control, information security, mathematics, and physical sciences. In this study, strength of artificial intelligence (AI) algorithms are explored for stochastic numerical computing for nonlinear fractional Rossler differential system by introducing state of art transformation in the radial basis neural networks (RNFN). Fractional order complex chaotic dynamical system of Rossler model represented by nonlinear coupled fractional differential equations are numerically solved with state of art fourth order fractional Runge-Kutta solver for different scenarios of control parameter and these outcomes are mensurate as reference solutions to model implementing RBFN with the different initial conditions of the chaotic dynamics. The innovative transformations are introduced to enhance the fast convergence of machine learning RBFN algorithm achieved through bimodal chaotic parameters. Performance of designed computing RBFN is authenticated efficaciously by RMSE metric for fractional order chaotic model of Rossler attractor with outcomes matching of the order of 10 to 15 decimal places in term of accuracy as compared to standard results computed from fractional Runge-Kutta solver. It is believed the proposed AI knacks based research work will open new innovative path in fractional order modelling and analysis of natural chaotic dynamic systems.