Global stability and Neimark-Sacker bifurcation of a host-parasitoid model

Qamar Din

International Journal of Systems Science, 2017, vol. 48, issue 6, 1194-1202

Abstract: We investigate qualitative behaviour of a density-dependent discrete-time host-parasitoid model. Particularly, we study boundedness of solutions, existence and uniqueness of positive steady-state, local and global asymptotic stability of the unique positive equilibrium point and rate of convergence of modified host-parasitoid model. Moreover, it is also proved that the system undergoes Neimark-Sacker bifurcation with the help of bifurcation theory. Finally, numerical simulations are provided to illustrate theoretical results. These results of numerical simulations demonstrate chaotic long-term behaviour over a broad range of parameters. The computation of the maximum Lyapunov exponents confirm the presence of chaotic behaviour in the model.

Date: 2017
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DOI: 10.1080/00207721.2016.1244308

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