Open AccessGlobal existence and stability of the classical solution to a density-dependent prey-predator model with indirect prey-taxis
Author(s) -
Yong Luo
Publication year - 2021
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2021331
Subject(s) - predation , taxis , population , lyapunov function , mathematics , functional response , predator , instability , constant (computer programming) , stability (learning theory) , statistical physics , biological system , control theory (sociology) , ecology , biology , physics , mechanics , computer science , botany , demography , control (management) , nonlinear system , quantum mechanics , machine learning , artificial intelligence , sociology , programming language
We study the existence of global unique classical solution to a density-dependent prey-predator population system with indirect prey-taxis effect. With two Lyapunov functions appropriately constructed, we then show that the solution can asymptotically approach prey-only state or coexistence state of the system under suitable conditions. Moreover, linearized analysis on the system at these two constant steady states shows their linear instability criterion. By numerical simulation we find that some density-dependent prey-taxis and predators' diffusion may either flatten the spatial one-dimensional patterns which exist in non-density-dependent case, or break the spatial two-dimensional distribution similarity which occurs in non-density-dependent case between predators and chemoattractants (released by prey).