Global Attractivity in a Nonlinear Difference Equation
نویسندگان
چکیده
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 mathematical biology.
منابع مشابه
Global 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 کاملBoundedness and Global Attractivity of a Higher-Order Nonlinear Difference Equation
We investigate the local stability, prime period-two solutions, boundedness, invariant intervals, and global attractivity of all positive solutions of the following difference equation: yn 1 r pyn yn−k / qyn yn−k , n ∈ N0, where the parameters p, q, r ∈ 0,∞ , k ∈ {1, 2, 3, . . .} and the initial conditions y−k, . . . , y0 ∈ 0,∞ . We show that the unique positive equilibrium of this equation is ...
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 کاملOn the Dynamic of a Nonautonomous
Nonlinear difference equations of higher order are important in applications; such equations appear naturally as discrete analogues of differential and delay differential equations which model various diverse phenomena in biology, ecology, economics, physics and engineering. The study of dynamical properties of such equations is of great importance in many areas. The autonomous difference equat...
متن کاملGlobal attractivity in a quadratic-linear rational difference equation with delay
Global attractivity in a quadratic-linear rational difference equation with delay C.M. Kent & H. Sedaghat To cite this article: C.M. Kent & H. Sedaghat (2009) Global attractivity in a quadratic-linear rational difference equation with delay, Journal of Difference Equations and Applications, 15:10, 913-925, DOI: 10.1080/10236190802040992 To link to this article: http://dx.doi.org/10.1080/1023619...
متن کامل