A computational study of fractional variable-order nonlinear Newton–Leipnik chaotic system with radial basis function network

This research study involves modeling Newton–Leipnik attractors within the domain of fractional variable-order (FVO) dynamics using a nonlinear and adaptable radial basis function neural network (RBFNN). The numerical solution for the FVO Newton–Leipnik system is initially obtained using a numerical scheme based on the Caputo–Fabrizio derivative with variable order. This process is carried out across a range of different control parameters. A parametric model is also constructed using RBFNN, considering various system initial values. Multiple instances of chaos are calculated using a proposed computational model within the Newton–Leipnik system with varying fractional-order functions. This investigation aims to assess and comprehend the extent of sensitivity exhibited by chaotic behavior achieved through the computation of Lyapunov exponents. The performance of the proposed computational RBFNN model is validated using the RMSE statistic. The results closely align with those obtained through numerical algorithms based on the Caputo–Fabrizio derivative, demonstrating the high accuracy of the designed network.