In this paper, we have proved several theorems which guarantee that the Lienard equation has at least one or n limit cycles without using the traditional assumption G Thus some results in [3-5] are extended. The limit...In this paper, we have proved several theorems which guarantee that the Lienard equation has at least one or n limit cycles without using the traditional assumption G Thus some results in [3-5] are extended. The limit cycles can be located by our theorems. Theorems 3 and 4 give sufficient conditions for the existence of n limit cycles having no need of the conditions that the function F(x) is odd or 'nth order compatible with each other' or 'nth order contained in each other'.展开更多
A class of recharge–discharge oscillator model for the El Ni？o/Southern Oscillation （ENSO） is considered. A stable limit cycle is obtained by transforming the ENSO model into the van der Pol-Duffing equation. We p...A class of recharge–discharge oscillator model for the El Ni？o/Southern Oscillation （ENSO） is considered. A stable limit cycle is obtained by transforming the ENSO model into the van der Pol-Duffing equation. We proved that there exists periodic oscillations in the ENSO recharge–discharge oscillator model.展开更多
文摘In this paper, we have proved several theorems which guarantee that the Lienard equation has at least one or n limit cycles without using the traditional assumption G Thus some results in [3-5] are extended. The limit cycles can be located by our theorems. Theorems 3 and 4 give sufficient conditions for the existence of n limit cycles having no need of the conditions that the function F(x) is odd or 'nth order compatible with each other' or 'nth order contained in each other'.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.40975028 and 41175052)
文摘A class of recharge–discharge oscillator model for the El Ni？o/Southern Oscillation （ENSO） is considered. A stable limit cycle is obtained by transforming the ENSO model into the van der Pol-Duffing equation. We proved that there exists periodic oscillations in the ENSO recharge–discharge oscillator model.
