Bistability and Bifurcations in Modified Nicholson-Bailey Model with Age-Structure for Prey

A predator prey model with age structure.

A general predator-prey model is considered in which the predator population is assumed to have an age structure which significantly affects it fecundity. The model equations are derived from the general McKendrick equations for age structured populations. The existence, stability and de-stabilization of equilibria are studied as they depend on the prey's natural carrying capacity and the matur...

Heteroclinic Foliation, Global Oscillations for the Nicholson-bailey Model and Delay of Stability Loss

This paper is concerned with the classical Nicholson-Bailey model [15] defined by fλ(x, y) = (y(1 − e−x), λye−x). We show that for λ = 1 a heteroclinic foliation exists and for λ > 1 global strict oscillations take place. The important phenomenon of delay of stability loss is established for a general class of discrete dynamical systems, and it is applied to the study of nonexistence of periodi...

The Dynamical Analysis of a Delayed Prey-Predator Model with a Refuge-Stage Structure Prey Population

A mathematical model describing the dynamics  of a  delayed  stage structure prey - predator  system  with  prey  refuge  is  considered.  The  existence,  uniqueness  and bounded- ness  of  the  solution  are  discussed.    All  the  feasibl e  equilibrium  points  are determined.  The   stability  analysis  of  them  are  investigated.  By  employ ing  the time delay as the bifurcation parame...

Bifurcations and Chaos in a Periodic Predator-Prey Model

Bistability, Bifurcations, and Waddington's Epigenetic Landscape

Waddington's epigenetic landscape is probably the most famous and most powerful metaphor in developmental biology. Cells, represented by balls, roll downhill through a landscape of bifurcating valleys. Each new valley represents a possible cell fate and the ridges between the valleys maintain the cell fate once it has been chosen. Here I examine models of two important developmental processes -...