Qualitative analysis of a multimolecules model. (Chinese. English summary) Zbl 0755.92026
Summary: The author studies a multi-molecular model:
\[
dx/dt=1-xy^ q,\quad dy/dt=ay(xy^{q-1}-1)\quad (a>0, q\geq 2).\tag{*}
\]
He obtains the following result: There exists an \(a^*\in(1/(q-1),a_ 0)\) such that if \(a\in(1/(q-1),a^*)\), then (*) has a unique stable limit cycle; if \(a\geq a^*\) or \(a\leq 1/(q-1)\), then (*) has no limit cycle.
MSC:
| 92E99 | Chemistry |
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
