Empirical evidence, obtained from nonparametric estimation of the income distribution, exhibits strong heterogeneity in most populations of interest. It is common, therefore, to suspect that the population is composed of several homogeneous subpopulations. Such an assumption leads us to consider mixed income distributions whose components feature the distributions of the incomes of a particular...

By using the upperand lower-solution method of partial functional differential equations and the oscillation theory of functional differential equation, the oscillation of a population equation with diffusion and delay is studied and a sufficient condition for all positive solutions of the equation to oscillate about the positive equilibrium is obtained. Finally, a model arising from ecology is...

where x 1 and x 2 are functions of two species, respectively; h and k are harvesting terms standing for the harvests (see [1, 2]). Because of the effect of changing environment such as the weather, season, and food, the number of species population periodically varies with the time. The rate of change usually is not a constant. Motivated by this, we consider the periodic nonautonomous populatio...

The goal of this article is to illustrate several interesting bifurcations that can arise in population biology. These are of interest since it is often through bifurcation phenomena that changes significant enough to be measured occur. For example, a minor change in some environmental parameter can cause a system to change from being at rest to oscillating. We illustrate here the role of sever...

A stochastic version of the classical predatorprey population model is considered through a simple birthdeath formulation. The expected value of the process is obtained and shown to correspond to the deterministic predatorprey population model.

is known as Hutchinson’s equation, if r and K are positive constants and h(t) = t− τ for a positive constant τ. Hutchinson’s equation has been investigated by several authors (see, e.g., [13, 14, 18, 23]). Delay logistic equation (1.1) was studied by Gopalsamy and Zhang [7, 25] who gave sufficient conditions for the oscillation and the nonoscillation of (1.1). Publications [1, 2, 3, 4, 5, 6, 10...

This paper deals with a model for an age-sex structured population consisting of male, single and fertilized female subclasses taking into account a random coupling of sexes (for a period of mating only) and females' pregnancy. For certain forms of the demographic rates there are presented separable solutions, and the asymptotic behaviour of the general solution is demonstrated.

We propose a new approach for solving fractional partial differential equations based on a nonlinear fractional complex transformation and the general Riccati equation and apply it to solve the nonlinear time fractional biological population model and the (4+1)-dimensional space-time fractional Fokas equation. As a result, some new exact solutions for them are obtained.This approach can be suit...

A metapopulation model is presented for species which can reach high population densities per patch, and for which migration is such a frequent event that it influences local patch dynamics. Depending on the local dynamics chosen and the way patch extinction is modelled, there can exist stable and bi-stable situations. The model is compared to winking-patch models, and single population models....