Consider the generalized mixed RayleighLinard oscillator equations given by x = y, y = x

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Consider the generalized mixed Rayleigh–Liénard oscillator equations given by

˙ x = y, ˙ y = −x − a1y − b30x3 − b21x2y − b41x4y − b03y3.

Prove that at most three small-amplitude limit cycles can be bifurcated from the origin.

214 9. Local and Global Bifurcations

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