Nonlinear generalization of the isotonic oscillator via symmetrized potential yields an amplitude-dependent period expressible in terms of the hypergeometric function that reduces to 2π at α=1.
Cveticanin and T Pog´ any, Oscillator with a sum of noninteger-order nonlinearities , Journal of Applied Mathematics Volume 2012, Article ID 649050, 20 p ages
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On purely nonlinear oscillators generalizing an isotonic potential
Nonlinear generalization of the isotonic oscillator via symmetrized potential yields an amplitude-dependent period expressible in terms of the hypergeometric function that reduces to 2π at α=1.