Solutions of fractional-stochastic Bao's system

Journal Article

2020

Published in: 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.

• Volume Number: 59
• Issue Number: 3
• Magazine \ Newspaper: ALEXANDRIA ENGINEERING JOURNAL
• Pages: 1485-1493