The diffusive intraguild predation model with intraspecific competition and double free boundaries

Abstract

The purpose of this paper is to investigate a diffusive intraguild predation model with intraspecific competition and double free boundaries in one-dimensional space. By adapting existing techniques, we first prove the existence and uniqueness, regularity and uniform estimates of global solution. Then, in terms of parameters range, we show that a spreading-vanishing dichotomy for this free boundary problem. The long time behaviors of $(R,N,P)$ and criteria for spreading and vanishing are also obtained. Additionally, when spreading happens, we propose an upper bound and a lower bound for the asymptotic spreading speeds of the free boundaries. Moreover, numerical simulations are provided to confirm our theoretical results. This paper is an improvement and extension of literatures [Zhang DW, Dai BX. A free boundary problem for the diffusive intraguild predation model with intraspecific competition. J Math Anal Appl. 2019;474:381–412; Zhang DW, Dai BX. Spreading and vanishing in a diffusive intraguild predation model with intraspecific competition and free boundary. Math Methods Appl Sci. 2019;42:6917–6943].

Keywords:

• Diffusive intraguild predation model
• free boundary
• spreading and vanishing dichotomy
• criteria
• asymptotic spreading speeds

MSC (2010) Classifications:

• 35K51
• 35R35
• 92B05
• 35B40

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (No. 11871475).