Population growth and environment as a self-organizing system.
Population Growth and Persistence in a Heterogeneous Environment: the Role of Diffusion and Advection
The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional reaction-diffusion-advection equations, for the growth of a population on a heterogeneous habitat. Considering a number of models of increasing complexity we investigate the often contrary roles of advection and diffusion for the persistence of the population. When it is possible we demonstrate...
Population growth and the environment: Can we eat the cake and have it?
Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies
Resistance to chemotherapies, particularly to anticancer treatments, is an increasing medical concern. Among the many mechanisms at work in cancers, one of the most important is the selection of tumor cells expressing resistance genes or phenotypes. Motivated by the theory of mutation-selection in adaptive evolution, we propose a model based on a continuous variable that represents the expression level of a resistance gene (or genes, yielding a phenotype) influencing in healthy and tumor cells birth/death...
Population-size-dependent branching processes.
Positive almost automorphic solutions for some nonlinear delay integral equations.
Positive almost periodic solutions of non-autonomous delay competitive systems with weak allee effect.
Positive global solutions for a general model of size-dependent population dynamics.
Positive periodic solution for ratio-dependent -species discrete time system
In this paper, sharp a priori estimate of the periodic solutions is obtained for the discrete analogue of the continuous time ratio-dependent predator-prey system, which is governed by nonautonomous difference equations, modelling the dynamics of the competing preys and one predator having nonoverlapping generations. Based on more precise a priori estimate and the continuation theorem of the coincidence degree, an easily verifiable sufficient criterion of the existence of positive periodic solutions...
Positive periodic solutions for a predator-prey model with time delays and impulsive effect.
Positive periodic solutions for an impulsive ratio-dependent predator-prey system with delays.
Positive periodic solutions for nonlinear difference equations via a continuation theorem.
Positive periodic solutions of a discrete mutualism model with time delays.
Positive periodic solutions of functional differential equations and population models.
Positive periodic solutions of functional discrete systems and population models.
Positive periodic solutions of neutral logistic difference equations with multiple delays.
Positive solutions of a neutral difference equation with positive and negative coefficients.
Positive solutions of a renewal equation
An existence theorem is proved for the scalar convolution type integral equation .
Positive solutions of nonlinear delay integral equations modelling epidemics and population growth.
Possibly Longest Food Chain: Analysis of a Mathematical Model
We consider the number of trophic levels in a food chain given by the equilibrium state for a simple mathematical model with ordinary differential equations which govern the temporal variation of the energy reserve in each trophic level. When a new trophic level invades over the top of the chain, the chain could lengthen by one trophic level. We can derive the condition that such lengthening could occur, and prove that the possibly longest chain is globally stable. In some specific cases,...