In this paper we consider the permanence of the following Lotka᎐Volterra Ž . Ž . Ä w discrete competition system with delays k , k , l , and l : .x4 l . We show the system is permanent for all nonnegative integers k , k , l , and 2 1 2 1 l , if and only if -1 and -1 hold. ᮊ 2001 Academic Press 2 1
Necessary and Sufficient Conditions for Permanence and Global Stability of a Lotka–Volterra System with Two Delays
✍ Scribed by Yasuhisa Saito; Tadayuki Hara; Wanbiao Ma
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 198 KB
- Volume
- 236
- Category
- Article
- ISSN
- 0022-247X
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📜 SIMILAR VOLUMES
This paper presents the necessary and sufficient condition for the global stability of the following Lotka-Volterra cooperative or competition system with time delays: It is showed that the positive equilibrium of the system is globally asymptotically stable for all delays τ ij ≥ 0 i j = 1 2 if and
Al~a~et--Let a real polynomial in a complex variable, whose coefficients are any given continuous functions of two real interval parameters, be given. Necessary and sufficient conditions are derived for the polynomial to have all its zeros outside (or inside) the unit circle of the complex variable