In this article, we discuss the existence as well as global attractivity and ultimate positivity of solutions for a certain nonlinear first order ordinary differential equation on the unbounded intervals of real line via a classical fixed point theorem of Schauder (Smart [12, page 15]). Our hypotheses and claims have also been explained with the help of two realizations under some natural condi...

In 1 , the general nonautonomous n-species Lotka-Volterra competitive systems with impulsive effects are investigated. By using the methods of inequalities estimate and constructing the suitable Liapunov functions, the sufficient conditions on the permanence of whole species and global attractivity of systems are established. In 2 , the authors studied the following general nonautonomous n-spec...

In this paper, we present some alternative results concerning with the existence and attractivity dependence of solutions for a class of nonlinear fractional functional differential equations. In our consideration, we apply the well-known Schauder fixed point theorem in conjunction with the technique of measure of noncompactness. Moreover, we provide examples to illustrate the effectiveness of ...

In this paper, we investigate the relationship between Lp stability and internal stability of nonlinear systems. It is shown that under certain conditions, Lp stability without finite gain implies attractivity of the equilibrium, and that local Lp stability with finite gain implies local asymptotic stability of the origin.

We describe a prediction method called “Attractivity Weighting” (AW). In the case of cue-based paired comparison tasks, AW predicts a weighted average of the cue values of the most successful cues. In many situations, AW’s prediction is based on the cue value of the most successful cue, resulting in behavior similar to Take-the-Best (TTB). Unlike TTB, AW has a desirable characteristic called “a...

A threshold dynamics and global attractivity of positive steady state are established in terms of principal eigenvalues for a nonlocal reaction-diffusion population model with stage structure, and the effects of spatial dispersal and maturation period on the evolutionary behavior are also discussed in two specific cases.

We find some new results regarding the existence, uniqueness, boundedness, stability and attractivity of the solutions of a class of initialboundary-value problems characterized by a quasi-linear third order equation which may have non-autonomous forcing terms. The class includes equations arising in superconductor theory, quantum mechanics and in the theory of viscoelastic materials.

We study the solutions and attractivity of the difference equation xn+1 = axn−(2k+2) −a + 2k+2 ∏ i=0 xn−i for n = 0, 1, 2, ... where a, x−(2k+2),x−(2k+1),..., x0 are the real numbers, x−(2k+2)x−(2k+1)... x0 = a, and k ∈ Z. Mathematics Subject Classification: 39A10, 39A12