In this paper, we study the existence of monotone positive solutions which converge to the equilibrium of a nonlinear difference equation. Recently, there has been a lot of interest in studying such solutions and the existence of some specific solutions see 1–20 . In 8 , Karakostas and Stević studied the boundedness, global attractivity, and oscillatory and asymptotic periodicity of the nonnega...

This paper gives sufficient conditions for the practical and finite time stability of a particular class of linear discrete time delay systems. Analyzing the finite time stability concept, these new delay-independent conditions are derived using an approach based on the Lyapunov–like functions. The practical and attractive practical stability for discrete time delay systems has been investigate...

We consider strongly coupled quasilinear reaction-diiusion systems subject to nonlinear boundary conditions. Our aim is to develop a geometric theory for this type of equations. Such a theory is necessary in order to describe the dynamical behavior of solutions. In our main result we establish the existence and attractivity of center manifolds under suitable technical assumptions. The technical...

We construct and investigate local invariant manifolds for a large class of quasilinear parabolic problems with fully nonlinear dynamical boundary conditions and study their attractivity properties. In a companion paper we have developed the corresponding solution theory. Examples for the class of systems considered are reaction–diffusion systems or phase field models with dynamical boundary co...

We consider strongly coupled quasilinear reaction-di↵usion systems subject to nonlinear boundary conditions. Our aim is to develop a geometric theory for these types of equations. Such a theory is necessary in order to describe the dynamical behavior of solutions. In our main result we establish the existence and attractivity of center manifolds under suitable technical assumptions. The technic...

Our aim in this paper is to investigate the global attractivity of all positive solutions of the higher order nonlinear difference equation xn+1 = a+ bxn A−∑k i=0 bixn−i , n = 0, 1, . . . , where A, b, bk ∈ (0,∞), a, b0, . . . , bk−1 ∈ [0,∞), k ∈ {1, 2, . . .} and the initial conditions x−k, . . . , x0 are arbitrary. We show that one positive equilibrium of the equation is a global attractor wi...

In this paper, we establish the global attractivity of the positive steady state of the diffusive Nicholson’s equation with homogeneous Neumann boundary value under a condition that makes the equation a nonmonotone dynamical system. To achieve this, we develop a novel method: combining a dynamical systems argument with maximum principle and some subtle inequalities. © 2008 Elsevier Inc. All rig...

We consider a Leslie predator-prey system with mutual interference and feedback controls. For general nonautonomous case, by using differential inequality theory and constructing a suitable Lyapunov functional, we obtain some sufficient conditions which guarantee the permanence and the global attractivity of the system. For the periodic case, we obtain some sufficient conditions which guarantee...

For a class of scalar delay differential equations with impulses and satisfying a Yorke-type condition, criteria for the global asymptotic stability of the zero solution are established. These equations possess a non-delayed feedback term, which will be used to refine the general results on stability presented in recent literature. The usual requirements on the impulses are also relaxed. As an ...

Abstract The artificial light sources are useful tools for sampling night active insects, however, they also possess potential environmental risks in their habitats. To test applicability and evaluate risk caddisflies (Trichoptera), the attractivity of different portable traps working with LED, UV mixed-white was studied compared traditionally used mercury-vapour lamp (in Jermy-type trap), whic...