On the homoclinic orbits in a class of two-degree-of-freedom systems under the resonance conditions
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A class of two-degree-of-freedom systems in resonance with an external, parametric excitation is investigated, the existence of the periodic solutions locked to Ω is proved by the use of the method of multiple scales. This systems can be transformed into the systems of Wiggins under some conditions. A calculating formula which determines the existence of homoclinic orbits of the systems is given.
Key wordsa two-degree-of-freedom system method of multiple scales periodic solution homoclinic orbit chaos
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