Volume- 3
Issue- 4
Year- 2016
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Jawad Mahmoud Jassim , Maithem Hassen Kareem
This manuscript presents a new technique to derive an accurate describe of sporadically perturbed primary bifurcations in two non-linearly coupled oscillators in both the nonresonant and resonant cases. Statistical methodologies traditionally used by behavioral scientists assume that variables are continuous and linearly related. (Thom.C., 1975) has shown mathematically that catastrophe theory is an appropriate methodology to examine discontinuous non-linear relationships. While Thorn developed the theory to deal primarily with biological problems, (Zeeman, 1975) has explained how this approach can be effective with behavioral science phenomena. Catastrophe theory allows examination of discontinuous effects occurring over time.The bifurcations in the subharmonic resonant case are Z2-symmetry ones and they have codimension 3. On the other hand, the bifurcations in the main resonant case are shown to possess no symmetry properties and their codimension increases to 5. These bifurcation problems are analyzed in detail and the quasiglobal bifurcation classifications as well as bifurcation diagrams in the system are presented. It is shown that one can control vibration in non-linear systems with an appropriate choice of system parameters as suggested by some regions in the hyper surface where the amplitude of bifurcating solution is always zero.
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