In this paper we prove that the mixing time of a broad class of evolutionary dynamics in finite, unstructured populations is roughly logarithmic in the size of the state space. An important special case of such a stochastic process is the Wright-Fisher model from evolutionary biology (with selection and mutation) on a population of size N over m genotypes. Our main result implies that the mixin...

A general nonlinear age-structure predator-prey model is analyzed for the dynamics of two interacting populations that includes self-limitation on the prey and juvenile predation. Our aim is to identify mechanisms of newborn survival that allow us to explain viable interactions between the two populations in circumstances when their absence would otherwise result in unstable behavior with unbou...

We study the behavior of an infinite system of ordinary differential equations modeling the dynamics of a metapopulation, a set of (discrete) populations subject to local catastrophes and connected via migration under a mean field rule; the local population dynamics follow a generalized logistic law. We find a threshold below which all the solutions tend to total extinction of the metapopulatio...

In this paper, the confidence interval for the solution of stochastic exponential population growth model where the so-called parameter, population growth rate is not completely definite and it depends on some random environmental effects is obtained. We use Iran population data in the period 1921-2006 as an example.

The aim of this paper is to study a predator-prey population model which takes into account the uncertainty that arises when determining the initial populations of predator and prey . This model is solved numerically by means of a 4-order Runge-Kutta method. Simulations are made and a graphical representation is also provided to show the evolution of both populations over time. In addition to t...

A fundamental problem in population dynamics is to study uniform persistence of the ecosystems, that is, to study the long term survival of interacting species. Abstract persistence theory, started in [BFW, BW], has been well-developed for both continuous and discrete semi-dynamical systems (see, e.g., [FRT, HW, FS, HS1, Th2, YR]) and has been applied to various types of equations including rea...

We develop a dynamic system model for a population of water boilers, which is simple enough for control purposes, but at the same time appreciates the complexity of the boilers internal dynamics and the volatility of such a load. For this purpose, a computationally involved model for a single water boiler is improved and then used to create a population. Based on these boilers a simple Markov C...