Abstract
The present paper presents an extension of Melnikov's theory for the differential equation with complex function. The sufficient condition for the existence of a homoclinic orbit in the solutions of a perturbed equation is given. The method shown in the paper is used to derive a precursor criterion for chaos. Suitable conditions are defined for the parameters of equations for which the equation possesses a strange attractor set. The analytical results are compared with numerical ones, and a good agreement is found between them.
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Cveticanin, L. Extension of Melnikov criterion for the differential equation with complex function. Nonlinear Dyn 4, 139–152 (1993). https://doi.org/10.1007/BF00045251
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DOI: https://doi.org/10.1007/BF00045251