A heterogeneous parasitic-mutualistic model of mistletoes and birds on a periodically evolving domain

Jie Wang; Jian Wang; Jiafeng Cao; Jie Wang; Jian Wang; Jiafeng Cao

doi:10.3934/mbe.2020347

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 6: 6678-6698. doi: 10.3934/mbe.2020347

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Research article

A heterogeneous parasitic-mutualistic model of mistletoes and birds on a periodically evolving domain

Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, China

Received: 23 July 2020 Accepted: 21 September 2020 Published: 28 September 2020

In this paper, a parasitic-mutualistic model of mistletoes and birds defined in a heterogneous and periodically evolving domain is comprehensively investigated to reveal some new dynamical phenomena caused by the domain evolution. By establishing the core spatial-temporal risk index R₀^B and R₀^M for birds population and mistletoes-birds population, respectively, the fundamental extinction, persistence and coexistence behaviors are studied, and distinguished by such indexes. Moreover, the impact of domain evolution on the viability of mistletoes is examined as well, and it is concluded that the average expansion of the domain can enhance mistletoes' transmission capability, therefore, pro-mote the viability of mistletoes, and vice versa. Finally, numerical simulations are also exhibited for some specific cases to verify the theoretical conclusions.
Citation: Jie Wang, Jian Wang, Jiafeng Cao. A heterogeneous parasitic-mutualistic model of mistletoes and birds on a periodically evolving domain[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 6678-6698. doi: 10.3934/mbe.2020347

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Abstract

In this paper, a parasitic-mutualistic model of mistletoes and birds defined in a heterogneous and periodically evolving domain is comprehensively investigated to reveal some new dynamical phenomena caused by the domain evolution. By establishing the core spatial-temporal risk index R₀^B and R₀^M for birds population and mistletoes-birds population, respectively, the fundamental extinction, persistence and coexistence behaviors are studied, and distinguished by such indexes. Moreover, the impact of domain evolution on the viability of mistletoes is examined as well, and it is concluded that the average expansion of the domain can enhance mistletoes' transmission capability, therefore, pro-mote the viability of mistletoes, and vice versa. Finally, numerical simulations are also exhibited for some specific cases to verify the theoretical conclusions.

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