In general, the three-step population master equation is used by physicists in many studies of diffusion processes of microscopic particles on one-dimensional lattices [1], but this simple discrete equation has extensive and interesting applications in other fields as well, most recently to Hubbell’s neutral theory in ecology [2]. In the following, we shall use a population interpretation. It r...

In this paper, we will introduce a method to find a numerical solution of nonlinear age-structured population model using second-kind Chebyshev polynomials. This method convert the nonlinear age-structured population models to an equivalent differential equation. We introduce two variable second-kind Chebyshev polynomials and their basic properties. These properties will be used to reduce the o...

We present a method for deriving necessary and sufficient conditions for the local stability of the TCP-RED congestion control. The analysis is based on a differential equation model of the system. One equation describes the dynamics of the TCP source population operating in the congestion avoidance phase. The TCP dynamics are driven by another differential equation representing the RED control...

The Verhulst model is probably the best known macroscopic rate equation in population ecology. It depends on two parameters, the intrinsic growth rate and the carrying capacity. These parameters can be estimated for different populations and are related to the reproductive fitness and the competition for limited resources, respectively. We investigate analytically and numerically the simplest p...

In this work, we analyzed the impact of interventions on populations which exhibit unimodal dynamics. The six landmarks that characterize the “shape” of the unimodal reproduction curve   f x of the difference equation,   1 n n X f X   , are defined and used in order to examine and determine the behavior of dynamics of populations. By using the Li-Yorke criterion for determination of chaos...

We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the density with a kernel describing attractive-repulsive social interactions. The kernel’s first moment and its limiting behavior at the origin determine whether t...

for some r-dimensional vector of functions m(zi, θ) of the observable data vector zi and possible parameter value θ in some parameter space Θ. Assuming that θ0 is the unique solution of this population moment equation (equivalent to identification when only (*) is imposed), a method-of-moments estimator θ̂ is defined as a solution (or near-solution) of a sample analogue to (*), replacing the pop...

 The population structure of Aphanius anatoliae in Lake Eğirdir-Isparta-Turkey was studied, using 522 fish monthly in 2008. This study were observed in the number of individuals of each sex, age, weight and size compositions. In addition, the total length-weight relationship was calculated as well as the Von Bertalanffy growth equation. A study of the food uptake throughout the year has been ca...