Open AccessStability analysis of a complex four species food-web model
Author(s) -
Ashok Mondal,
A. K. Pal,
G. P. Samanta
Publication year - 2022
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2201099m
Subject(s) - mathematics , equilibrium point , hopf bifurcation , food web , stability (learning theory) , extinction (optical mineralogy) , parametric statistics , predation , bifurcation , apex predator , bifurcation theory , type (biology) , differential equation , control theory (sociology) , ecology , mathematical analysis , statistics , computer science , nonlinear system , artificial intelligence , biology , paleontology , physics , control (management) , quantum mechanics , machine learning
This paper aims to study the dynamical behaviours of a four dimensional food web system consisting of a bottom prey, two middle predators and a superpredator(top predator) with Holling Type I and Type II functional responses. A system of four differential equations has been proposed and analyzed. Positivity, boundedness and extinction criteria of the system are studied. We have discussed the existence of various equilibrium points and stability of the system at these equilibrium points. We also explore the system undergoes a Hopf-bifurcation around interior equilibrium point for a parametric values which has very significant ecological impacts in this work. Computer simulation are carried out to validate our analytical findings. The biological implications of analytical and numerical findings are discussed critically.