Extinction of top-predator in a three-level food-chain model

Abstract

Abstract. In this paper we extend the Lyapunov functions, constructed by A. Ardito and P. Ricciardi for predator-prey system [1], to the three level food chain models. We first consider a general three-level food-chain model. A criterion for the extinction of top predator will be given. Then we restrict our attentions to the case in which the prey is of logistic growth and predators have Holling's type II functional responses.

A ratio-dependent food chain model and its applications to biological control

“…prey-dependent) three species food chain model. Chiu and Hsu [25] discussed the extinction of top predator in a classical three-level food chain model with Michaelis-Menten functional response. Hastings and Powell [26], Klebanoff and Hastings [27,28], McCann and Yodzis [29], Kuznetsov and Rinaldi [30], Muratori and Rinaldi [31] and others studied structures relevant to chaos in three species classical food chains.…”

Qualitative effects of introducing nonlinear birth and death rates for the predator in a predator-prey type model

“…Proof: We shall construct a Lyapunov function for the system (4), using ideas, proposed in [1] and [3]. Let us define…”

Bifurcation and Stability Analysis of a Food Web in a Chemostat

“…Consequently, the persistence or uniformly persistence analysis has been applied to describe the situation when all interacting individuals coexist in a given system. A tri-tropic level food-chain model is considered in (Chiu and Hsu, 1998). They restricted their attentions to study when the prey grows logistically in the absence of predator and the functional responses of predators are of Holling's type II and established the criterion where the top-predator goes extinct globally.…”