Dynamics Analysis of a New Fractional-Order Hopfield Neural Network with Delay and Its Generalized Projective Synchronization

Entropy

Fei-Long Xie¹  Han-Ping Hu¹  Jia-Kun Wang¹ 

[1] School of Automation, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan 430074, China;

关键词: dynamics analysis;    fractional-order;    Hopfield neural network;    generalized projective synchronization;   

DOI  :  10.3390/e21010001

来源: DOAJ

【 摘 要 】

In this paper, a new three-dimensional fractional-order Hopfield-type neural network with delay is proposed. The system has a unique equilibrium point at the origin, which is a saddle point with index two, hence unstable. Intermittent chaos is found in this system. The complex dynamics are analyzed both theoretically and numerically, including intermittent chaos, periodicity, and stability. Those phenomena are confirmed by phase portraits, bifurcation diagrams, and the Largest Lyapunov exponent. Furthermore, a synchronization method based on the state observer is proposed to synchronize a class of time-delayed fractional-order Hopfield-type neural networks.

【 授权许可】

Unknown