Open AccessExploring the dynamics of a tritrophic food chain model with multiple gestation periods
Author(s) -
Ranjit Kumar Upadhyay,
Srikanta Mishra,
Yue Ping Dong,
Yasuhiro Takeuchi
Publication year - 2019
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.2019234
Subject(s) - hopf bifurcation , phase portrait , chaotic , mathematics , bifurcation , stability (learning theory) , control theory (sociology) , statistical physics , complex dynamics , mathematical analysis , computer science , physics , nonlinear system , control (management) , quantum mechanics , artificial intelligence , machine learning
This work is mainly focused on the series of dynamical analysis of tritrophic food chain model with Sokol-Howell functional response, incorporating the multiple gestation time delays for more realistic formulation. Basic properties of the proposed model are studied with the help of boundedness, stability analysis, and Hopf-bifurcation theory. By choosing the fixed parameter set and varying the value of time delay, the stability of the model has been studied. There is a critical value for delay parameter. Steady state is stable when the value of delay is less than the critical value and further increase the value of delay beyond the critical value makes the system oscillatory through Hopf-bifurcation. Whereas, another delay parameter has a stabilizing effect on the system dynamics. Chaotic dynamics has been explored in the model with the help of phase portrait and sensitivity on initial condition test. Numerical simulations are performed to validate the effectiveness of the derived theoretical results and to explore the various dynamical structures such as Hopf-bifurcation, periodic solutions and chaotic dynamics.