Chaos in Discrete Structured Population Models

Chaos in Discrete Structured Population Models

We prove analytically the existence of chaotic dynamics in some classical discrete-time age-structured population models. Our approach allows us to estimate the sensitive dependence on the initial conditions, regions of initial data with chaotic behavior, and explicit ranges of parameters for which the considered models display chaos. These properties have important implications for evaluating ...

Dynamics of Stage-structured Discrete Mosquito Population Models

We formulate discrete-time stage-structured models, based on systems of difference equations, for mosquito populations. We include the four distinct mosquito metamorphic stages, egg, pupa, larva, and adult, in the models. We derive a formula for the inherent net reproductive number, and investigate existence and stability of fixed points. We also show that the models, by means of numerical simu...

Entropy methods for linear discrete and continuous structured population models

The lectures are devoted to the methods of generalised relative entropy applied to study long-term behaviour of structured population models. Such models describe processes of growth and evolution of a population, which is heterogenous in respect to some physiological properties, such as age, size or stage of cell differentiation, which in turn influence dynamics of the individuals. Analysis of...

Chaos in a Discrete Delay Population Model

A Note on the Convergence of the Homotopy Analysis Method for Nonlinear Age-Structured Population Models

In this paper, a theorem is proved which presents the series solution obtained from the homotopy analysis method is convergent to the exact solution of nonlinear age-structured population models.