Analysis of a tritrophic food chain model with fear effect incorporating prey refuge

In this work, we have introduced a tritrophic food-chain model where consumer hunt for prey with Holling type-III functional response. The birth rate of the population has been reduced due to fear predation, i.e., effect is considered in population. Moreover, fraction available consumption and done by incorporation refuge term. predation between predator follows Beddington-DeAngelis Boundedness positivity system prove that proposed well-posed. Also, there are some parametric restrictions under which permanent. Routh-Hurwitz criterion shows local stability conditions equilibrium points on other hand Lyapunov LaSalle theorem guarantees locally stable globally stable. Matlab validates analytical results help diagrams. occurrence transcritical bifurcations shown existence limit cycle through Hopf bifurcation also stated. Both numerical suggest certain amount can make steady. It noted both stabilizing destabilizing system.