Global stability in a population model with piecewise constant arguments

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:360

Article

Gurcan, F.²  Bozkurt, F.¹ 

[1] Erciyes Univ, Fac Educ, Dept Math, TR-38039 Kayseri, Turkey

[2] Erciyes Univ, Fac Sci & Arts, Dept Math, TR-38039 Kayseri, Turkey

关键词: Logistic differential equations;    Difference equations;    Global stability;    Boundedness;    Semi-cycle solutions;   

DOI  :  10.1016/j.jmaa.2009.06.058

来源: Elsevier

【 摘 要 】

In this paper, we investigate the global stability and the boundedness character of the positive solutions of the differential equation dx/dt = r . x(t){1 - alpha . x(t) - beta(0)x([t]) - beta(1)x([t - 1])} where t >= 0, the parameters r, alpha, beta(0) and beta(1) denote positive numbers and [t] denotes the integer part of t is an element of [0, infinity). We considered the discrete solution of the logistic differential equation to show the global asymptotic behavior and obtained that the unique positive equilibrium point of the differential equation is a global attractor with a basin that depends on the conditions of the coefficients. Furthermore, we studied the semi-cycle of the positive solutions of the logistic differential equation. (c) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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