A Density-Dependent Host-Parasitoid Model with Stability, Bifurcation and Chaos Control

Xiaorong Ma, Qamar Din, Muhammad Rafaqat, Nasir Javaid and Yongliang Feng
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Xiaorong Ma: Office of School Enterprise Cooperation and Innovation and Entrepreneurship Education, Shaanxi Vocational and Technical College, Xi’an 710038, China
Qamar Din: Department of Mathematics, The University of Poonch Rawalakot, Azad Kashmir 10250, Pakistan
Muhammad Rafaqat: Department of Mathematics and Statistics, The University of Lahore, Lahore 54000, Pakistan
Nasir Javaid: Abdus Salam School of Mathematical Sciences, Lahore 54000, Pakistan
Yongliang Feng: School of information Engineering, Xi’an University, Xi’an 710065, China

Mathematics, 2020, vol. 8, issue 4, 1-26

Abstract: The aim of this article is to study the qualitative behavior of a host-parasitoid system with a Beverton-Holt growth function for a host population and Hassell-Varley framework. Furthermore, the existence and uniqueness of a positive fixed point, permanence of solutions, local asymptotic stability of a positive fixed point and its global stability are investigated. On the other hand, it is demonstrated that the model endures Hopf bifurcation about its positive steady-state when the growth rate of the consumer is selected as a bifurcation parameter. Bifurcating and chaotic behaviors are controlled through the implementation of chaos control strategies. In the end, all mathematical discussion, especially Hopf bifurcation, methods related to the control of chaos and global asymptotic stability for a positive steady-state, is supported with suitable numerical simulations.

Keywords: host-parasitoid model; stability analysis; Neimark-Sacker bifurcation; chaos control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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