Open AccessBoundedness and stabilization of a predator-prey model with attraction- repulsion taxis in all dimensions
Author(s) -
Wenbin Lyu
Publication year - 2022
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.2022629
Subject(s) - bounded function , taxis , mathematics , constant (computer programming) , domain (mathematical analysis) , norm (philosophy) , uniform boundedness , convergence (economics) , boundary (topology) , mathematical analysis , lyapunov function , attraction , computer science , nonlinear system , physics , economics , philosophy , transport engineering , political science , engineering , programming language , economic growth , quantum mechanics , linguistics , law
This paper establishes the existence of globally bounded classical solutions to a predator-prey model with attraction-repulsion taxis in a smooth bounded domain of any dimensions with Neumann boundary conditions. Moreover, the global stabilization of solutions with convergence rates to constant steady states is obtained. Using the local time integrability of the L 2 -norm of solutions, we build up the basic energy estimates and derive the global boundedness of solutions by the Moser iteration. The global stability of constant steady states is established based on the Lyapunov functional method.