On the Liénard system with two isoclines

Year, pages: 2009, 505 - 515

In this paper, the non-existence of limit cycles of a Liénard system $\dot{x}=y-F(x)$, $\dot{y}=-g(x)$ is discussed. By using the transformation $y=z+\varphi(x)$ to the system, the new system has two special isoclines. We call the curves Vertical isocline or Horizontal isocline, respectively. It shall be shown that the existence of these isoclines play an important role in the non-existence of limit cycles of the system. The results are applied to many examples, and the known results are improved in certain cases.

Hayashi, M. 2009. On the Liénard system with two isoclines. In Mathematica Slovaca, vol. 59, no.4, pp. 505-515. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0144-1

Hayashi, M. (2009). On the Liénard system with two isoclines. Mathematica Slovaca, 59(4), 505-515. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0144-1