The limit cycles of the generalized Rayleigh-Lie´nard oscillator X + AX + 2BX 3 + o(z 3 + z 2 X 2 + z 1 X 4 + z 4 X 2 )X = 0, for A q 0, B q 0, and A Q 0, B q 0 are studied by using the Jacobian elliptic functions with the generalized harmonic balance method. For given values of the parameters z i $
✦ LIBER ✦
THE NUMBER OF LIMIT CYCLES FOR THE GENERALIZED MIXED RAYLEIGH-LIÉNARD OSCILLATOR
✍ Scribed by J. Burnette; R.E. Mickens
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 276 KB
- Volume
- 188
- Category
- Article
- ISSN
- 0022-460X
No coin nor oath required. For personal study only.
✦ Synopsis
The generalized Rayleigh and van der Pol differential equations are given, respectively, by the following expressions [1-5]:
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We consider a class of planar differential equations which include the Lie´nard differential equations. By applying the Bendixson-Dulac Criterion for '-connected sets we reduce the study of the number of limit cycles for such equations to the condition that a certain function of just one variable do