A novel fractional-order hyperchaotic system with a quadratic exponential nonlinear term and its synchronization

Advances in Difference Equations

Mohammad Reza Modabbernia¹  Masoud Taleb Ziabari²  Ali Reza Sahab³ 

[1] Electrical Engineering Department, Rasht Branch, Technical and Vocational University, Rasht, Iran;Faculty of Engineering, Computer Engineering Group, Ahrar University, Rasht, Iran;Faculty of Engineering, Electrical Engineering Group, Lahijan Branch, Islamic Azad University, Lahijan, Iran

关键词: novel fractional-order hyperchaotic system;    generalized backstepping method;    synchronization;    genetic algorithm;    cuckoo optimization algorithm;    particle swarm optimization algorithm;    imperialist competitive algorithm;    cost function;   

DOI  :  10.1186/1687-1847-2012-194

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The dynamics of fractional-order systems have attracted increasing attention in recent years. In this paper a novel fractional-order hyperchaotic system with a quadratic exponential nonlinear term is proposed and the synchronization of a new fractional-order hyperchaotic system is discussed. The proposed system is also shown to exhibit hyperchaos for orders 0.95. Based on the stability theory of fractional-order systems, the generalized backstepping method (GBM) is implemented to give the approximate solution for the fractional-order error system of the two new fractional-order hyperchaotic systems. This method is called GBM because of its similarity to backstepping method and more applications in systems than it. Generalized backstepping method approach consists of parameters which accept positive values. The system responses differently for each value. It is necessary to select proper parameters to obtain a good response because the improper selection of parameters leads to inappropriate responses or even may lead to instability of the system. Genetic algorithm (GA), cuckoo optimization algorithm (COA), particle swarm optimization algorithm (PSO) and imperialist competitive algorithm (ICA) are used to compute the optimal parameters for the generalized backstepping controller. These algorithms can select appropriate and optimal values for the parameters. These minimize the cost function, so the optimal values for the parameters will be found. The selected cost function is defined to minimize the least square errors. The cost function enforces the system errors to decay to zero rapidly. Numerical simulation results are presented to show the effectiveness of the proposed method.

【 授权许可】

CC BY