A general discrete time model of population dynamics in the presence of an infection.
A note on stabilization of discrete nonlinear systems.
A trichotomy result for non-autonomous rational difference equations
We study non-autonomous rational difference equations. Under the assumption of a periodic non-autonomous parameter, we show that a well known trichotomy result in the autonomous case is preserved in a certain sense which is made precise in the body of the text. In addition we discuss some questions regarding whether periodicity preserves or destroys boundedness.
Almost periodic solutions of prey-predator discrete models with delay.
Almost sufficient and necessary conditions for permanence and extinction of nonautonomous discrete logistic systems with time-varying delays and feedback control
A class of nonautonomous discrete logistic single-species systems with time-varying pure-delays and feedback control is studied. By introducing a new research method, almost sufficient and necessary conditions for the permanence and extinction of species are obtained. Particularly, when the system degenerates into a periodic system, sufficient and necessary conditions on the permanence and extinction of species are obtained. Moreover, a very important fact is found in our results, that is, the feedback...
Alternate derivations of the stability region of a difference equation with two delays.
An analysis of the stability boundary for a linear fractional difference system
This paper deals with basic stability properties of a two-term linear autonomous fractional difference system involving the Riemann-Liouville difference. In particular, we focus on the case when eigenvalues of the system matrix lie on a boundary curve separating asymptotic stability and unstability regions. This issue was posed as an open problem in the paper J. Čermák, T. Kisela, and L. Nechvátal (2013). Thus, the paper completes the stability analysis of the corresponding fractional difference...
Annular bounds for polynomial zeros and Schur stability of difference equations.
Approximation of limit cycle of differential systems with variable coefficients
The behavior of the approximate solutions of two-dimensional nonlinear differential systems with variable coefficients is considered. Using a property of the approximate solution, so called conditional Ulam stability of a generalized logistic equation, the behavior of the approximate solution of the system is investigated. The obtained result explicitly presents the error between the limit cycle and its approximation. Some examples are presented with numerical simulations.
Asymptotic Solutions of nonlinear difference equations
We study the asymptotics of first-order nonlinear difference equations. In particular we present an asymptotic functional equation for potential asymptotic behaviour, and a theorem stating sufficient conditions for the existence of an actual solution with such asymptotic behaviour.
Asymptotic stability for a class of nonlinear difference equations.
Boundedness and global attractivity of a higher-order nonlinear difference equation.
Boundedness and stability for discrete-time delayed neural network with complex-valued linear threshold neurons.
Competitive Exclusion in a Discrete Stage-Structured Two Species Model
We develop a stage-structured model that describes the dynamics of two competing species each of which have sexual and clonal reproduction. This is typical of many plants including irises. We first analyze the dynamical behavior of a single species model. We show that when the inherent net reproductive number is smaller than one then the population will go to extinction and if it is larger than one then an interior equilibrium exists and it is globally asymptotically stable. Then we analyze...
Complete asymptotic and bifurcation analysis for a difference equation with piecewise constant control.
Dynamical properties in a fourth-order nonlinear difference equation.
Dynamics for nonlinear difference equation .
Dynamics in a discrete predator-prey system with infected prey
In this paper, a discrete version of continuous non-autonomous predator-prey model with infected prey is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and the method of Lyapunov function, some sufficient conditions for the existence and global asymptotical stability of positive periodic solution of difference equations in consideration are established. An example shows the feasibility of the main results.
Dynamics of a higher-order nonlinear difference equation.
Dynamics of a rational system of difference equations in the plane.