Co-existence of a Period Annulus and a Limit Cycle in a Class of Predator-Prey Models with Group Defense

For a family of two-dimensional predator-prey models of Gause type, we investigate the simultaneous occurrence of a center singularity and a limit cycle. The family is characterized by the fact that the functional response is nonanalytical and ehibits group defense. We prove the eistence and uniqueness of the limit cycle using a new theorem...

Several Bifurcation Mechanisms for Limit Cycles in a Predator–Prey System

The research presented in this paper compares the occurrence of limit cycles under different bifurcation mechanisms in a simple system of two-dimensional autonomous predator–prey ODEs. Surprisingly two unconventional approaches, for a singular system and for a system with a center, turn out to produce more limit cycles than the traditional...

Singular perturbations of the Holling I predator-prey system with a focus

We study the occurrence of limit cyles in a model for two-species predator-prey interaction (referred to as Holling I). This model is based on the phenomenological fitting of the so-called functional response function to observed data in nature by a continuous, piecewise differentiable function. Of the original models presented by Holling it...

Predator-prey models with non-analytical functional response

In this paper we study the generalized Gause model, with a logistic growth rate for the prey in absence of the predator, a constant death rate for the predator and for several different classes of functional response, all non-analytical. First we consider the piecewise-linear functional response of Holling type I, which essentially has a...

A Linear Method for Shape Reconstruction based on the Generalized Multiple Measurement Vectors Model

In this paper, a novel linear method for shape reconstruction is proposed based on the generalized multiple measurement vectors (GMMV) model. Finite difference frequency domain (FDFD) is applied to discretized Maxwell’s equations, and the contrast sources are solved iteratively by exploiting the joint sparsity as a regularized...

Extension of the GMMV-based Linear Method to Quantitative Inverse Scattering

The linear shape reconstruction method based on the generalized multiple measurement vectors model is a newly proposed approach which is able to effectively retrieve the morphological information of dielectric/metallic scatterers with competitive imaging resolution. In this letter, we have extended this approach to quantitative inversion, and...