title: Hybrid control of the Neimark-Sacker bifurcation in a delayed Nicholson's blowflies equation.
abstract: In this article, for delayed Nicholson's blowflies equation, we propose a hybrid control nonstandard finite-difference (NSFD) scheme in which state feedback and parameter perturbation are used to control the Neimark-Sacker bifurcation. Firstly, the local stability of the positive equilibria for hybrid control delay differential equation is discussed according to Hopf bifurcation theory. Then, for any step-size, a hybrid control numerical algorithm is introduced to generate the Neimark-Sacker bifurcation at a desired point. Finally, numerical simulation results confirm that the control strategy is efficient in controlling the Neimark-Sacker bifurcation. At the same time, the results show that the NSFD control scheme is better than the Euler control method.
authors.affiliation: College of Science, China University of Petroleum (East China), Qingdao, 266580 P.R. China.
authors.forename: Yuanyuan
authors.initials: Y
authors.lastname: Wang
authors.affiliation: School of Science, Qingdao Technological University, Qingdao, 266033 P.R. China.
authors.forename: Lisha
authors.initials: L
authors.lastname: Wang
keywords: Neimark-Sacker bifurcation; Nicholson’s blowflies equation; delay; hybrid control; nonstandard finite-difference scheme