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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 657245, 9 pages
http://dx.doi.org/10.1155/2013/657245
Research Article

Nonlinear Dynamics and Chaos in Fractional-Order Hopfield Neural Networks with Delay

1Shandong Key Laboratory of Robotics and Intelligent Technology, College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao 266590, China
2College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China

Received 4 August 2013; Accepted 30 September 2013

Academic Editor: Changpin Li

Copyright © 2013 Xia Huang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A fractional-order two-neuron Hopfield neural network with delay is proposed based on the classic well-known Hopfield neural networks, and further, the complex dynamical behaviors of such a network are investigated. A great variety of interesting dynamical phenomena, including single-periodic, multiple-periodic, and chaotic motions, are found to exist. The existence of chaotic attractors is verified by the bifurcation diagram and phase portraits as well.