On the uniqueness of the limit cycle of the generalized Liénard equation. (English) Zbl 0805.34031
In this paper we consider the generalized Lienard equation (1) \({dx \over dt} = \varphi (y) - F(x)\), \({dy \over dt} = - g(x)\). We collect a series of lemmas which are useful from estimating the characteristic exponent \(h = - \int_ L f(x(t))dt\), (where \(f(x) = F'(x))\) of a closed orbit \(L\) of system (1). By these lemmas some uniqueness theorems of limit cycle are proved, which generalize many known results.
Reviewer: Zhang Zhifen (Beijing)
MSC:
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
| 37G15 | Bifurcations of limit cycles and periodic orbits in dynamical systems |
| 34C25 | Periodic solutions to ordinary differential equations |
