Limit Cycles in a General Nonlinear Oscillation

 


Xuncheng Huang

 

Department of Mathematics

Yangzhou Polytechnic University

20 Mountain Tiger Road, 2-403

Yangzhou, Jiangsu 225002, China

 

 

Abstract: Theorems on the existence and uniqueness of limit cycles in the general nonlinear oscillation have been studied.  The conditions that guarantee the uniqueness of limit cycles here are different from all the previous results.  Several examples are given to illustrate that the theorems are easy to be employed, and they are useful in the discussion of limit cycles in quadratic differential equations and ecological systems.

 

Keywords: limit cycles; Liénard equation; nonlinear oscillation; ecological systems.

 

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