Permanence for a generalized discrete neural network system.
Permanence of a discrete model of mutualism with infinite deviating arguments.
Permanence of a discrete -species Schoener competition system with time delays and feedback controls.
Permanence of a discrete nonlinear prey-competition system with delays.
Permanence of a discrete periodic Volterra model with mutual interference.
Permanence of a discrete predator-prey system with Beddington-DeAngelis functional response and feedback controls.
Perron-type criterion for linear difference equations with distributed delay.
Perturbation method for linear difference equations with small parameters.
Phases of linear difference equations and symplectic systems
The second order linear difference equation where and , is considered as a special type of symplectic systems. The concept of the phase for symplectic systems is introduced as the discrete analogy of the Borůvka concept of the phase for second order linear differential equations. Oscillation and nonoscillation of (1) and of symplectic systems are investigated in connection with phases and trigonometric systems. Some applications to summation of number series are given, too.
Plus-operators in Krein spaces and dichotomous behavior of irreversible dynamical systems with discrete time
We study dichotomous behavior of solutions to a non-autonomous linear difference equation in a Hilbert space. The evolution operator of this equation is not continuously invertible and the corresponding unstable subspace is of infinite dimension in general. We formulate a condition ensuring the dichotomy in terms of a sequence of indefinite metrics in the Hilbert space. We also construct an example of a difference equation in which dichotomous behavior of solutions is not compatible with the signature...
PM functions, their characteristic intervals and iterative roots
The concept of characteristic interval for piecewise monotone functions is introduced and used in the study of their iterative roots on a closed interval.
Poisson kernels of drifted Laplace operators on trees and on the half-plane
Starting with the computation of the appropriate Poisson kernels, we review, complement, and compare results on drifted Laplace operators in two different contexts: homogeneous trees and the hyperbolic half-plane.
Polylogarithms in the field of omega (a root of given cubic): Functional equations and ladders.
Polynomial set-valued functions
The aim of this paper is to give a necessary and sufficient condition for a set-valued function to be a polynomial s.v. function of order at most 2.
Population Dynamics of Grayling: Modelling Temperature and Discharge Effects
We propose a matrix population modelling approach in order to describe the dynamics of a grayling (Thymallus thymallus, L. 1758) population living in the Ain river (France). We built a Leslie like model, which integrates the climate changes in terms of temperature and discharge. First, we show how temperature and discharge can be related to life history traits like survival and reproduction. Second, we show how to use the population model to precisely examine the life cycle of grayling : estimated...
Positive and bounded solutions of discrete reaction-diffusion equations.
Positive decreasing solutions of higher-order nonlinear difference equations.
Positive fixed point theorems arising from seeking steady states of neural networks
Biological systems are able to switch their neural systems into inhibitory states and it is therefore important to build mathematical models that can explain such phenomena. If we interpret such inhibitory modes as `positive' or `negative' steady states of neural networks, then we will need to find the corresponding fixed points. This paper shows positive fixed point theorems for a particular class of cellular neural networks whose neuron units are placed at the vertices of a regular polygon. The...
Positive periodic solution for ratio-dependent -species discrete time system
In this paper, sharp a priori estimate of the periodic solutions is obtained for the discrete analogue of the continuous time ratio-dependent predator-prey system, which is governed by nonautonomous difference equations, modelling the dynamics of the competing preys and one predator having nonoverlapping generations. Based on more precise a priori estimate and the continuation theorem of the coincidence degree, an easily verifiable sufficient criterion of the existence of positive periodic solutions...
Positive periodic solutions of abstract difference equations.