Dynamical analysis of a new three-dimensional fractional chaotic system

Pramana: Journal of physics

P GHOLAMIN^1¹ 

[1] Department of AppliedMathematics, Faculty of Mathematical Sciences, Lahijan Branch, Islamic Azad University, Lahijan, Iran^1

关键词: New fractional chaotic system;    Grünwald–Letnikov derivative;    stability conditions;    fractional Hopf bifurcation;    numerical simulations;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In the present paper, a new fractional chaotic system proposed by the authors is discussed. Moreover, based on the stability theory of fractional-order systems, conditions for the stability of nonlinear fractional-order systems are presented, and the existence and uniqueness of the solutions of the resulting new fractional chaotic attractor are also studied. Next, the necessary conditions for the existence of chaotic attractors in new fractionalchaotic system are reported, and at the end the stability analysis of the corresponding equilibria is given. Last but not the least, the presented numerical simulations confirm the validity of our analysis.

【 授权许可】

CC BY