Global attractivity and oscillation in a nonlinear periodic delay difference equation
نویسندگان
چکیده
منابع مشابه
Global Attractivity in a Nonlinear Difference Equation
In this paper, we study the asymptotic behavior of positive solutions of the nonlinear difference equation xn+1 = xnf(xn−k), where f : [0,∞)→ (0,∞) is a unimodal function, and k is a nonnegative integer. Sufficient conditions for the positive equilibrium to be a global attractor of all positive solutions are established. Our results can be applied to to some difference equations derived from ma...
متن کاملGlobal Attractivity in Nonlinear Delay Difference Equations
We obtain a set of sufficient conditions under which all positive solutions of the nonlinear delay difference equation x„+l = x„f(xn_k), n = 0,1,2,..., are attracted to the positive equilibrium of the equation. Our result applies, for example, to the delay logistic model JVI+i = aN¡/(\ +ßNt_k) and to the delay difference equation xn+i = x„er^~x"-k'1 .
متن کاملGlobal Attractivity and Oscillations in a Periodic Delay - Logistic Equation
in which r and K are positive numbers; r is related to the reproduction of the species while K is related to the capacity of the environment to sustain the population. It is assumed that there is no immigration or emigration and other characteristics such as age dependence and interactions with other species are assumed to be not significant. Elementary analysis of (1.1) indicates that the solu...
متن کاملGlobal Attractivity and Periodic Nature of a Difference Equation
Our goal in this paper is to investigate the global stability character and the periodicity of the solutions of the difference equation Where the initial conditions x ,x ,...,x are arbitrary positive real numbers, r = max{l, k} is nonnegative integer –r –r+1 0 and a, b, c, d are positive constants.
متن کاملGlobal attractivity of a higher-order nonlinear difference equation
In this paper, we investigate the global attractivity of negative solutions of the nonlinear difference equation xn+1 = 1− xn−k A + xn , n = 0, 1, . . . , where A ∈ (−∞, 0), k is a positive integer and initial conditions x−k, · · · , x0 are arbitrary real numbers. We show that the unique negative equilibrium of abovementioned equation is a global attractor with a basin under certain conditions....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2003
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(03)00067-1