Global asymptotic stability in a rational recursive sequence

Yang, X. F., Lai, H. J., Evans, D. J. and Megson, G. M. (2004) Global asymptotic stability in a rational recursive sequence. Applied Mathematics and Computation, 158 (3). pp. 703-716. ISSN 0096-3003 doi: 10.1016/j.amc.2003.10.010

Abstract/Summary

In this paper, we study the global stability of the difference equation x(n) = a + bx(n-1) + cx(n-1)(2)/d - x(n-2), n = 1,2,....., where a, b greater than or equal to 0 and c, d > 0. We show that one nonnegative equilibrium point of the equation is a global attractor with a basin that is determined by the parameters, and every positive Solution of the equation in the basin exponentially converges to the attractor. (C) 2003 Elsevier Inc. All rights reserved.