Solutions of fractional-stochastic Bao's system
al., Korpinar, Zeliha; Tchier, Fairouz; Inc, Mustafa; et . 2020
Systems of high-dimensional nonlinear ordinary differential equations play a significant
role in Physics and applied sciences including big-data optimization, financial models, epidemic disease
models. In this paper, we are concerned with numerical solutions of Bao’s system that is a 4-
dimensional hyperchaotic system introduced by Bo-Cheng and Zhong (2008). We solve the Bao’s
system with both the Crank-Nicolson and power series methods. Crank-Nicolson method is eventually
evolved into a new system whose solution is presented in a quite neat algorithmic manner. By
adding standard Brownian motion to each term in the model, we express the Bao’s system as a system
of stochastic differential equations. We solve the stochastic system with an Euler-type approximate
solution method. By adding noise and expressing time derivatives with Caputo-type fractional
derivative, we study on synchronization and parameter estimation of the models. To the best of our
knowledge, Bao’s system has not been numerically solved with the methods employed in this paper
previously, and this paper considers fractional and stochastic Bao’s system for the first time in the
history of research. Techniques employed by us in this paper may serve as a framework for solutions
of many other systems of ordinary differential equations including Lorenz types and epidemic
models.
Systems of high-dimensional nonlinear ordinary differential equations play a significant
role in Physics and applied sciences including big-data optimization, financial models, epidemic…