We consider the dynamical system x ttt = c 2 − 1 2 x 2 − x t for the parameter c close to zero. We perform a multiple timescale analysis to provide analytic forms for all bounded solutions of the formal normal form in the phase space, in a neighbourhood of the origin (x, c) = (0, 0). These take the form of Jacobi elliptic functions describing periodic and quasi-periodic solutions, and hyperbolic functions that describe heteroclinic connections. A comparison between these approximate analytical results and numerical simulations of the unperturbed system shows excellent correspondence.
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