A study of the chaotic features of variable order fractional Liu’s system via radial basis neural network

Variable-order differential operators can be useful for modeling chaotical systems and nonlinear fractional differential equations. In this work, we report on a study of the fractional variable domain behavior of the Liu attractor. We employ a flexible and nonlinear radial basis function network (RBFN) structure to model this complicated system. First, we use a numerical scheme for the fractional Liu’s system in the Caputo–Fabrizio sense to calculate the physical characteristics of the complex fractional variable order system. We investigate multiple random scenarios of control restrictions and create a parametric model for a range of chaotic Liu’s system initial circumstances. Then, 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 fractional variable-order 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. The average mutual information method is employed to calculate the fractional variable-order system’s embedded dimension and time delay to evaluate the appropriateness of the time delay chaotic pattern in the fractional variable domain. 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 fractional variable order domain.