This paper discusses several issues related to blind source separation in nonlinear models. Specifically, separability results show that separation in the general case is impossible, however, for specific nonlinear models the problem does have a solution. A specific set of parametric nonlinear mixtures is considered, this set has the Lie group structure. In the parameter set, a group operation ...

Following ecologists discoveries, mathematicians have begun studying extensions of the ubiquitous age structured Leslie population model to allow some survival probabilities and/or fertility rates depend on population densities. These nonlinear extensions commonly exhibit very complicated dynamics: through computer studies, some authors have discovered robust Hénon-like strange attractors in se...

The internal zero-stabilization of the nonnegative solution to a nonlinear age-dependent population model with diffusion is investigated in this paper. It is provided here a necessary condition and a sufficient condition for the nonnegative zerostabilizability in terms of the value of the principal eigenvalue to a certain elliptic operator. This principal eigenvalue is related to the rate of th...

In this article, we derive Ricker’s [22, 23] type nonlinear boundary condition for an age structured population dynamic model by using a singular perturbation. The question addressed in this paper is the convergence of the singularly perturbed system. We first obtain a finite time convergence for a fixed initial distribution. Then we focus on the convergence uniformly of the singularly perturbe...

We consider an age-structured model of a harvested population. This model is a discrete-time system that includes a nonlinear stock-recruitment relationship. Our purpose is to estimate the stock state. To achieve this goal, we built an observer, which is an auxiliary system that uses the total number of fish caught over each season and gives a dynamical estimation of the number of fish by age c...

We extend results of Gouzé and Hadeler (in Nonlinear World 1:23-34, 1994) concerning the dynamics generated by a map on an ordered metric space that can be decomposed into increasing and decreasing parts. Our main results provide sufficient conditions for the existence of a globally asymptotically stable fixed point for the map. Applications to discrete-time, stage-structured population models ...

In this article, we study the dynamics of a new proposed age-structured population mathematical model driven by seasonal forcing function that takes into account variability climate. We introduce generalized force infection to different potential disease outcomes. Using nonlinear analysis tools and differential inequalities theorems, obtain sufficient conditions guarantee existence positive per...