The two-species population dynamics model is the simplest paradigm of interspecies interaction. Here, we include intraspecific competition to the Lotka-Volterra model and solve it analytically. Despite being simple and thoroughly studied, this model presents a very rich behavior and some characteristics not so well explored, which are unveiled. The forbidden region in the mutualism regime and t...

One of the best examples of traditional analysis of evolutionary stable strategies (ESS) is provided by the so called Dove-Hawk model. In this paper we present several enhancements to the model aimed at describing the evolution of cooperative behavior. In addition to Doves and Hawks we introduce several groups of Cooperators, who act as Doves within their own group, but as Hawks outside it. Thi...

The aim of the present work is two-fold: to develop numerical procedures for a priori determining whether a given cell population, having a distributed cell-cycle duration, will grow or decay when subjected to prescribed chemotherapy; to evaluate the cumulative error in the long-term predictions for such populations. We show that cell population dynamics under drug treatment can be modelled by ...

A common situation occurring in a number of disciplines is that in which a number of autonomous agents reach a consensus without a central direction. An example of this is the emergence of a common belief in a price system when activity takes place in a given market. Another example is the emergence of common languages in primitive societies, or the dawn of vowel systems. Yet a third example is...

In internal ethno-territorial conflicts, what explains why state or rebel group leaderships use civilian-targeting strategies—expulsion or mass killing strategies designed to punish enemy civilians or to decimate the enemy civilian presence on contested territory? One argument is that those living under the worst initial conditions—defined in terms of collective goods such as weak collective au...

where the parameters a, b, d, and e are positive numbers and the initial conditions x0 and y0 are arbitrary nonnegative numbers. In a modelling setting, system (1.1) of nonlinear difference equations represents the rule by which two discrete, competitive populations reproduce from one generation to the next. The phase variables xn and yn denote population sizes during the nth generation and the...

Positive density-dependence occurs when individuals experience increased survivorship, growth, or reproduction with increased population densities. Mechanisms leading to these positive relationships include mate limitation, saturating predation risk, and cooperative breeding and foraging. Individuals within these populations may differ in age, size, or geographic location and thereby structure ...

This paper presents two simple models for nonlinear age-dependent population dynamics. In these models the basic equations of the theory reduce to systems of ordinary differential equations. We discuss certain qualitative aspects of these systems; in particular, we show that for many cases of interest periodic solutions are not possible. 1. BASIC EQUATIONS Recently, Gurtin and MacCamy [l] intro...