Stability switches and Hopf bifurcations of an isolated population model with delay-dependent parameters

Min Xiao, Guoping Jiang, Lindu Zhao, Wenying Xu, Youhong Wan, Chunxia Fan and Zhengxin Wang

Applied Mathematics and Computation, 2015, vol. 264, issue C, 99-115

Abstract: The dynamical behaviors of an isolated population model involving delay-dependent parameters are investigated. It is shown that the positive equilibrium switches from being stable to unstable and then back to stable as the delay increases, and the Hopf bifurcation occurs finite times between the two critical values of stability changes which can be analytically determined. Moreover, the bifurcating periodic solutions are expressed analytically in an approximate form by the perturbation approach and Floquet technique. The direction and stability of the bifurcating periodic solutions are also determined. Finally, the validity of the results is shown by the consistency with the numerical simulations.

Keywords: Isolated population model; Delay; Stability switch; Hopf bifurcation; Perturbation approach; Floquet technique (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:264:y:2015:i:c:p:99-115

DOI: 10.1016/j.amc.2015.04.071

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