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Advances in Mathematical Physics
Volume 2016 (2016), Article ID 2028037, 8 pages
http://dx.doi.org/10.1155/2016/2028037
Research Article

Controlling Neimark-Sacker Bifurcation in Delayed Species Model Using Feedback Controller

School of Mathematics and Computer Science, Zunyi Normal College, Zunyi 563002, China

Received 16 June 2016; Accepted 10 July 2016

Academic Editor: Pavel Kurasov

Copyright © 2016 Jie Ran 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

Based on the stability and orthogonal polynomial approximation theory, the ordinary, dislocated, enhancing, and random feedback control methods are used to suppress the Neimark-Sacker bifurcation to fixed point in this paper. It is shown that the convergence rate of enhancing feedback control and random feedback control can be faster than those of dislocated and ordinary feedback control. The random feedback control method, which does not require any adjustable control parameters of the model, just only slightly changes the random intensity. Finally, numerical simulations are presented to verify the effectiveness of the proposed controllers.