Open AccessDynamics of the Stage Structured Population Model, Predator Accompanied by Michaelis Menten Holling Type Functional Responseand Delay and Prey Taking Refuge
Author(s) -
N. Mohana Sorubha Sundari
Publication year - 2021
Publication title -
türk bilgisayar ve matematik eğitimi dergisi
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.218
H-Index - 3
ISSN - 1309-4653
DOI - 10.17762/turcomat.v12i2.1950
Subject(s) - functional response , hopf bifurcation , mathematics , equilibrium point , lyapunov function , control theory (sociology) , stability (learning theory) , population , predation , type (biology) , bifurcation , predator , mathematical optimization , mathematical analysis , nonlinear system , computer science , ecology , differential equation , biology , control (management) , physics , demography , quantum mechanics , artificial intelligence , machine learning , sociology
The current work considers predator prey system, prey taking refuge, predator reckoned with time delay and Michaelis Menten Holling type II response function undergoing two stages: juvenile and mature. From the characteristic equation, we derive conditions for the local stability of the system at the equilibrium points. Also, at the coexistence equilibrium point, the system is analyzed for the occurrence of Hopf bifurcation. Lyapunov function provides sufficient conditions for the global stability of the system. Numerical simulations are given to support the theory.