Open AccessHopf bifurcation in an age-structured prey-predator model with Holling Ⅲ response function
Author(s) -
Lijun Wang,
Chuanjun Dai,
Min Zhao
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.2021156
Subject(s) - hopf bifurcation , mathematics , semigroup , functional response , predation , period (music) , bifurcation , stability (learning theory) , steady state (chemistry) , period doubling bifurcation , function (biology) , mathematical analysis , predator , control theory (sociology) , nonlinear system , physics , economics , ecology , computer science , biology , chemistry , acoustics , control (management) , quantum mechanics , machine learning , evolutionary biology , management
In this paper, we propose a prey-predator model with age structure which is described by the mature period. The aim of this paper is to study how mature period affect the dynamics of interaction between prey and predator. The sufficient condition of the existence of non-negative steady state is derived. By using integrated semigroup theory, we obtain the characteristic equation, by which we find that the non-negative steady state will lose its stability via Hopf bifurcation induced by mature period, and the corresponding periodic solutions emerge. Additionally, some numerical simulations are provided to illustrate the results predicted by linear analysis. Especially, the numerical results indicate that both mature period and age can affect the amplitude and period of periodic solutions.