Abstract
Extinction and coexistence of species are two fundamental issues in systems with IGP. In this paper, we constructed a mathematical model with IGP by introducing heterogeneous environment and B-D functional response between the predator and prey. First, some sufficient conditions for the extinction and permanence of the time-dependent system were obtained by using comparison principle and upper and lower solution method. Second, we got some necessary and sufficient conditions for the existence of coexistence states by means of the fixed point index theory. In addition, we discussed the uniqueness and stability of coexistence state under some conditions. Finally, we studied the effects of the parameters in system on the spatial distribution of species and obtained some interesting results about the extinction and coexistence of species by using numerical simulations.
Highlights
Intraguild predation, or IGP, is a widespread ecological phenomenon in natural communities, which occurs when two consumers share a common resource and engage in a predator-prey interaction [35, 36, 4]
Motivated by the articles above, we construct a mathematical model with heterogeneous environment by introducing the diffusion and B-D functional response between the predator and prey and obtain the following IGP system:
Most studies about predator and prey models with IGP were assumed in a homogeneous environment in space and different ODE models were set up
Summary
Intraguild predation, or IGP, is a widespread ecological phenomenon in natural communities, which occurs when two consumers share a common resource and engage in a predator-prey interaction [35, 36, 4]. To our knowledge, few model is constructed with assuming the B-D functional response between the predator and prey to investigate the IGP. On the other hand, [37] model IGP in a heterogeneous environment with space to be a continuous variable resulting in a parabolic system of PDEs with Neumann boundary condition They assumed that the IGprey employs a fitness based avoidance strategy and proved the existence of a global attractor for this system and derived conditions for the uniform persistence of the IGprey. Motivated by the articles above, we construct a mathematical model with heterogeneous environment by introducing the diffusion and B-D functional response between the predator and prey and obtain the following IGP system:. (4) It follows from Theorem 2.2 that there exists a unique positive solution of (4) if λ1,k(ρ(x)) < 0. For sufficiently small positive constant , there exists a T1( ) such that u(x, t) ≤
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
