Tohoku Mathematical Journal
2006

March
SECOND SERIES VOL. 58, NO. 1

Tohoku Math. J.
58 (2006), 89-100

Title ON DYNAMICS OF GENERALIZED COMPETITIVE AND COOPERATIVE SYSTEMS

Author Lihong Huang, Taishan Yi and Xingfu Zou

(Received February 10, 2004, revised April 15, 2005)
Abstract. In this paper, we are concerned with $n$-dimensional generalized competitive or cooperative systems of ordinary differential equations. A result is established to show that the flow generated by a generalized cooperative and irreducible system is strongly monotone. Also, it is shown that an analogue of the Poincare-Bendixon theorem holds for three dimensional generalized competitive and dissipative systems. Finally, we provide a generalized Smale's construction.

2000 Mathematics Subject Classification. Primary 34C25; Secondary 34K25, 34C12.

Key words and phrases. Competitive/cooperative system, Smale's construction, dynamics, arbitrary order cone.

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