一类周期互惠共存系统的正周期解POSITIVE PERIODIC SOLUTION OF A PERIODIC COOPERATIVE SYSTEM
崔景安,黄永年
摘要(Abstract):
本文考虑一类两种群周期互惠共存系统,应用拓扑度理论,得到了系统存在唯一的渐近稳定的正周期解的合理条件;并进一步证明了周期解的全局渐近稳定性,给出了解的最优上下界估计。
关键词(KeyWords): 互惠共存系统;周期解;全局渐近稳定性
基金项目(Foundation):
作者(Author): 崔景安,黄永年
参考文献(References):
- 1 May R M. Theoretical Ecology, Principles and Applications. Sounders Philadelphia, 1976
- 2 陈兰荪.数学生态学模型与研究方法.北京:科学出版社.1988
- 3 Golpalsamy K. Exchange of equilibria in two species Lotka-Volterra competition models. J Austral Math. Soc Ser B24, 1982: 160~170
- 4 Gopalsamy K. Global asymptotic stability in a periodic Lotka-Volterra system. J Austral Math Soc Ser B27, 1985: 66~72
- 5 Alvarez C, Lazer A C. An application of topological degree to the periodic competing species problem. J Austral Math Soc Ser, B28, 1986: 202~219
- 6 Shair Ahmad. Convergence and Ultimate Bounds of solutions of the Nonautonomous Volterra-Lotka Competition Equations. J Math Amal Appl, 1987; 127: 377~387
- 7 Lloyd N G. Degree theory. Cambirdge University Press, 1978
- 8 Coddington E A, Levinson N. Theory of ordinary differential equations. McGraw-Hill, New York, 1955
- 9 Hale J K. Ordinary differential equations, Wiley-Interscience, New York, 1969
- 10 Gantmacher F R. Applications of the theory of matrices. Interscienc, New York, 1959