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THE GREATEST NUMBER OF LIMIT CYCLES OF THE GENERALIZED RAYLEIGH–LIÉNARD OSCILLATOR

✍ Scribed by J.D. Bejarano; J. Garcia-Margallo

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
115 KB
Volume
221
Category
Article
ISSN
0022-460X

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✦ Synopsis

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 $ 0, i = 1, 2, 3, 4, the values of A and B for which limit cycles exist are found as functions of a single parameter. There is one limit cycle in the region where the Hamiltonian, E say, is positive, i.e., a solution of type cn, and six limit cycles, three double values, in the region where E is negative, solution type dn.

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