TY - JOUR

T1 - A two patch prey-predator model with multiple foraging strategies in predator

T2 - Applications to insects

AU - Messan, Komi

AU - Kang, Yun

N1 - Funding Information:
K.S.M is partially supported by the Department of Education GAANN (P200A120192). This research of Y.K. is partially supported by NSF-DMS (1313312); NSF- IOS/DMS (1558127) and The James S. McDonnell Foundation 21st Century Science Initiative in Studying Complex Systems Scholar Award (UHC Scholar Award 220020472). This research of Y.K. is partially supported by NSF-DMS (1313312); NSF- IOS/DMS (1558127) and The James S. McDonnell Foundation 21st Century Science Initiative in Studying Complex Systems Scholar Award (UHC Scholar Award 220020472). The research of K.M. is partially supported by the Department of Education GAANN (P200A120192). We would like to give a special appreciation to Marisabel Rodriguez and Daniel Burkow for their assistances. In addition, we really appreciate the useful comments from the referee to improve this work significantly.

PY - 2017/5

Y1 - 2017/5

N2 - We propose and study a two patch Rosenzweig-MacArthur prey-predator model with immobile prey and predator using two dispersal strategies. The first dispersal strategy is driven by the prey-predator interaction strength, and the second dispersal is prompted by the local population density of predators which is referred as the passive dispersal. The dispersal strategies using by predator are measured by the proportion of the predator population using the passive dispersal strategy which is a parameter ranging from 0 to 1. We focus on how the dispersal strategies and the related dispersal strengths affect population dynamics of prey and predator, hence generate different spatial dynamical patterns in heterogeneous environment. We provide local and global dynamics of the proposed model. Based on our analytical and numerical analysis, interesting findings could be summarized as follow: (1) If there is no prey in one patch, then the large value of dispersal strength and the large predator population using the passive dispersal in the other patch could drive predator extinct at least locally. However, the intermediate predator population using the passive dispersal could lead to multiple interior equilibria and potentially stabilize the dynamics; (2) The large dispersal strength in one patch may stabilize the boundary equilibrium and lead to the extinction of predator in two patches locally when predators use two dispersal strategies; (3) For symmetric patches (i.e., all the life history parameters are the same except the dispersal strengths), the large predator population using the passive dispersal can generate multiple interior attractors; (4) The dispersal strategies can stabilize the system, or destabilize the system through generating multiple interior equilibria that lead to multiple attractors; and (5) The large predator population using the passive dispersal could lead to no interior equilibrium but both prey and predator can coexist through fluctuating dynamics for almost all initial conditions.

AB - We propose and study a two patch Rosenzweig-MacArthur prey-predator model with immobile prey and predator using two dispersal strategies. The first dispersal strategy is driven by the prey-predator interaction strength, and the second dispersal is prompted by the local population density of predators which is referred as the passive dispersal. The dispersal strategies using by predator are measured by the proportion of the predator population using the passive dispersal strategy which is a parameter ranging from 0 to 1. We focus on how the dispersal strategies and the related dispersal strengths affect population dynamics of prey and predator, hence generate different spatial dynamical patterns in heterogeneous environment. We provide local and global dynamics of the proposed model. Based on our analytical and numerical analysis, interesting findings could be summarized as follow: (1) If there is no prey in one patch, then the large value of dispersal strength and the large predator population using the passive dispersal in the other patch could drive predator extinct at least locally. However, the intermediate predator population using the passive dispersal could lead to multiple interior equilibria and potentially stabilize the dynamics; (2) The large dispersal strength in one patch may stabilize the boundary equilibrium and lead to the extinction of predator in two patches locally when predators use two dispersal strategies; (3) For symmetric patches (i.e., all the life history parameters are the same except the dispersal strengths), the large predator population using the passive dispersal can generate multiple interior attractors; (4) The dispersal strategies can stabilize the system, or destabilize the system through generating multiple interior equilibria that lead to multiple attractors; and (5) The large predator population using the passive dispersal could lead to no interior equilibrium but both prey and predator can coexist through fluctuating dynamics for almost all initial conditions.

KW - Dispersal strategies

KW - Non-random foraging movements

KW - Passive dispersal

KW - Predation strength

KW - The Rosenzweig-MacArthur prey-predator model

UR - http://www.scopus.com/inward/record.url?scp=85014313084&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85014313084&partnerID=8YFLogxK

U2 - 10.3934/dcdsb.2017048

DO - 10.3934/dcdsb.2017048

M3 - Article

AN - SCOPUS:85014313084

VL - 22

SP - 947

EP - 976

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

IS - 3

ER -