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A trace identity is proposed and it is shown that this identity can be effectively applied to establish the Hamiltonian structure of the KP, DS hierarchies and a new hierarchy of ( 1 -I-2)dimensional systems.1900

ABSTRACT. In this paper, a Kolmogorov-type model, which includes the Gause-type model (Kuang and Freedman, 1988), the general predator-prey model (Huang 1988, Huang andMerrill 1989), and many other specialized models, is studied. The stability of equilibrium points, the existence and uniqueness of limit cycles in the model are proved.

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