Energy Variability and Chaos in Ueda Oscillator

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[Abstract] Use of Melnikov method enables us to prove the existence of transverse homoclinic points and homoclinic bifurcations occurring in a number of dynamical systems. Energy plays acrucial role in the description of the evolutionary behaviour of nonlinear dynamical systems. If the energy behaves like a variable; it leads us to an interesting way to understand results obtained in investigation of various systems. Melnikov function, that measures the distance between the stable and unstable manifolds of the saddlee quilibrium of the Poincare map of sections near the separatrix, has been associated with the energy variable of the Hamiltonian. The system used here is the Ueda oscillator, [3, 5, 12, 13], which displays very interesting results during evolution shown through these works. We have again investigated the Ueda oscillator and studied its chaotic and transient chaotic evolutions taking into account the concept of energy variability. With the adjustment of certain parameter, we have observed, the chaotic, transient chaotic and regular behaviour through phase plots and Poincare surface of sections. Numerical results are obtained to support the analytical calculations which are discussed through various graphics.

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