The paper presented a transient population dynamics of phase singularities in 2D Beeler-Reuter model. Two stochastic modelings are examined: (i) the Master equation approach with the transition rate (i.e., λ(n, t) = λ(t)n and μ(n, t) = μ(t)n) and (ii) the nonlinear Langevin equation approach with a multiplicative noise. The exact general solution of the Master equation with arbitrary time-depen...

In this paper, sufficient conditions are investigated for the existence of periodic (not necessarily positive) solutions for nonlinear several time delay population system with feedback control. Nonlinear system affected by an periodic external source is studied. Existence of a control variable provides  the extension of  some previous results obtained in other studies. We give a illustrative e...

In this work we suggest a simple mathematical model for the dynamics of the population of children and adolescents without problematic behavior (criminal activities etc.). This model represents a typical population growth equation but with time dependent (linearly decreasing) population growth coefficient. Given equation admits definition of the half-life time of the non-problematic children be...

In this paper we consider the null controllability for a population model depending on time, space and age. Moreover, diffusion coefficient degenerate at boundary of domain. The novelty is that first time presence memory term, which makes computations more difficult. However, under suitable condition kernel deduce result original problem via new Carleman estimates adjoint associated to nonhomog...

Abstract We establish the existence and uniqueness of global (in time) positive strong solutions for a generalized population dynamics equation with environmental noise, while fails deterministic equation. Particularly, we prove following stochastic differential d X t = ( θ m 0 + k ) e 1 2 φ W , > ⩾ x ∈ R being constants r ϑ or | log also show that index is sharp in sense if one can choose cert...