Food chains and webs in the environment can be modeled by systems of ordinary differential equations that approximate species or functional feeding group behavior with a variety of functional responses. We present here a new methodology for computing all equilibrium states and bifurcations of equilibria in food chain models. The methodology used is based on interval analysis, in particular an i...

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...

We show in this paper that the chaotic regimes of many food chain models often enjoy a very peculiar property, known as peak-to-peak dynamics. This means that the maximum (peak) density of the populations of any trophic level can be easily forecasted provided the last two peaks of the same population are known. Moreover, extensive simulation shows that only the last peak is needed if the foreca...

The adaptation of the most strains of the fungus Lecanicillium muscarium ZARE & GAMS to moderate temperatures and humidity higher 80% as well as the sensitiveness of the spores to UVradiation explains, that the application regime mainly takes place under protected conditions in greenhouses. Laboratory trials with a very effective strain for the use as biological control agent (strain V24, secti...

We provide an analytical proof of the existence of a stable periodic orbit contained in the region of coexistence of the three species of a tritrophic chain. The method used consists in analyzing a triple Hopf bifurcation. For some values of the parameters three limit cycles bear via this bifurcation. One is contained in the plane where the top–predator is absent. Another one is not contained i...