In this paper, the Homotopy perturbation method is successfully extended to solve fractional biological population model and numerical results are obtained. The fractional derivatives are described in the Caputo sense, some examples are provided. And the solutions of the equation are continuous with the parameter α . Mathematics subject classification (2010): 35D99.

Since its inception by Kimura in 1955 [M. Kimura, Proc. Natl. Acad. Sci. U.S.A. 41, 144 (1955)], the diffusion equation has become a standard technique of population genetics. The diffusion equation is however only an approximation, valid in the limit of large populations and small selection. Moreover, useful quantities such as the fixation probabilities are not easily extracted from it and nee...

We propose a computational approach to modeling the collective dynamics of populations of coupled heterogeneous biological oscillators. In contrast to Monte Carlo simulation, this approach utilizes generalized Polynomial Chaos (gPC) to represent random properties of the population, thus reducing the dynamics of ensembles of oscillators to dynamics of their (typically significantly fewer) repres...

Replicator-mutator equation is used to describe the dynamics of complex adaptive systems in population genetics, biochemistry and models of language learning. We study "localized", or "coherent", solutions, which are especially relevant in the context of learning and correspond to the existence of a predominant language in the population. There is a coherence threshold for learning fidelity, ab...

In this paper it is argued that evolutionary economics needs general statistical tools for performing the analysis of the aggregate effects of evolution in terms of the underlying population dynamics. These tools have been developed within biometrics, and they have recently become directly applicable to economic evolution due to the development of what may be called a general evometrics. Centra...

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Variable individual response to epidemics may be found within many contexts in the study of infectious diseases (e.g., age structure or contact networks). There are situations where the variability, in terms of epidemiological parameter, cannot be neatly packaged along with other demographics of the population like spatial location or life stage. Transport equations are a novel method for handl...

In this paper, we establish the existence of travelling wave solution to an intrinsically non-linear differential-integral equation formed as a result of mathematical modelling of the evolution of an asexual population in a changing environment. This equation is first converted to a non-linear integral equation. The discretization and manipulation of the corresponding eigenvalue problem allows ...

The distribution of neutron population in nuclear reactor is described by using transport equations. One of possible approximations of neutron transport equation is given by the neutron diffusion equation. The paper presents numerical solution method of one group neutron diffusion equation with one group of delayed neutrons.

In this work Peter principle (in the hierarchical structure any competent member tends to rise to his level of incompetence) is consistently interpreted as the discrete form of the well-known logistic (Verhulst or Maltusian) equation of the population dynamics. According to such interpretation anti-Peter principle (in the hierarchical structure any incompetent member tends to rise to his level ...