Stability and Neimark–Sacker bifurcation for a discrete Nicholson's blowflies model with proportional delay. Issue 2 (1st February 2021)

• Record Type: Journal Article
• Authors: Pan, Zhikang; Li, Xianyi
• Is Part Of: Journal of difference equations and applications. Volume 27:Issue 2(2021)
• Page Start: 250
• Page End: 260
• Publication Date: 2021-02-01
• Subjects: Discrete Nicholson's blowflies model with proportional delay -- semidiscretization method -- Neimark–Sacker bifurcation -- centre manifold theorem -- bifurcation theory; 39A10; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2021.1887159
• Languages: English
• ISSNs: 1023-6198

Abstract

Abstract : In this paper, we revisit a Nicholson's blowflies model with proportional delay, the stability and bifurcation of whose discrete version have not been studied. By using the method of semidiscretization, we dig deeply out the stability and Neimark–Sacker bifurcation of its discrete model. Especially, some results for the existence and stability of Neimark–Sacker bifurcation are derived by using the centre manifold theorem and bifurcation theory. Numerical simulations are also formulated to verify the existence of Neimark–Sacker bifurcation derived.