Existence and uniqueness of limit cycles on a cubic kolmogorov differential system in the Predator-Prey relation |
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| Authors: | Wanxuan Gan |
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| Institution: | (1) Yunnan Agricultural University, China |
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| Abstract: | In this paper, we analyse qualitatively a cubic Kolmogorov system:
![$$\left\{ \begin{gathered} \frac{{dx}}{{dt}} = xa_0 + a_1 x - a_3 x^2 - a_4 y + a_5 xy], \hfill \\ \frac{{dy}}{{dt}} = y(x - 1)(1 + by), \hfill \\ \end{gathered} \right.$$](/content/r03k7q0l73113205/10255_2005_Article_BF02006221_TeX2GIFIE1.gif)
which is one of the mathematical models in ecology describing the interaction between Predator-Prey of two populations; and give the conditions of nonexistence, existence and uniqueness of limit cycles for three different cases.Fulfilled during engagement in advanced studies at the Institute of Mathematics, Academia Sinica. |
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