Density dependent mortality and weak allee effect modulate the chaotic behaviour-a conclusion from a tri-trophic food chain study

Anuraj Singh; Krishna Pada Das; Binayak Nath; Subhabrata Ghosh

Anuraj Singh ABV-Indian Institute of Information Technology $\&$ Management, Gwalior 474015, India
Krishna Pada Das Mahadevananda Mahavidyalaya Department Of Mathematics Monirampore P.O.-Barrackpore Kol-120
Binayak Nath Mahadevananda Mahavidyalaya,\\ Monirampore, P.O.-Barrackpore, Kolkata 700108, India
Subhabrata Ghosh Mahadevananda Mahavidyalaya\\ Monirampore, P.O.-Barrackpore, Kolkata 700120, India

Abstract

Density dependent mortality and weak Allee effect are the two key regulators that alter the nature of the population dynamics of particular species in various important ways. An understanding of the mechanisms of these two factors can provide valuable understanding into the dynamics that can guide conservational plans in many ecological systems to restore the ecological balance. Here we represent a tri-trophic food chain framework accompanying density-dependent mortality in intermediate predator and weak Allee effect in prey species .
Criteria for local along with global stability behaviour of the equilibrium points are maintained.The occurrence of occasional solutions via Hopf bifurcation with regard to half-saturation constant is established.The extensive numerical simulations are carried out to interpret the dynamic behaviour of the system over a long time interval. Our simulation results depicts that the system exhibits chaotic pattern for increasing values of the half-saturation constant. Our results advice that chaos can be regulated by incorporating density-dependent mortality as well as by weak Allee effect.