Numerical Solutions of Chen Dynamical System by Quintic B-Spline Method

Abstract

We propose a novel method based on quintic B-spline functions to obtain numerical solutions of the three-dimensional Chen chaotic system. The Chen system has applications in secure communication, modeling complex natural processes, and image encryption, due to its chaotic and complex dynamics. It can also be used to design and analyze control systems, optimize performance, and study physical phenomena through its mathematical model. Due to its various applications, solutions of this dynamical system are very important. Building on cubic B-spline formulations, the method yields dynamical properties that confirm its high efficiency for such models. Chaotic systems are sensitive to initial conditions. This physical behaviour is very well captured by the proposed numerical scheme. Computed results have been presented in tabular forms and figures. All computations have been carried out in 5.11 Dev C++. For numerical simulations, Matlab software has been used