Abstract

PREDICTIONS AND DETECTIONS OF CHAOTIC BEHAVIOUR IN SINGLE AND DOUBLE WELL DUFFING OSCILLATOR UNDER CERTAIN PARAMETRIC VARIATIONS AND EXCITATIONS

Everestus Obinwanne Eze,1 Uchenna Emmanuel Obasi,2 Godwin Ezugorie3 and Ujumadu Rosary Ngozi4

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The synthesis of chaotic behaviors in single and double well Duffing oscillators under certain parametric variation and excitation were studied. The Melnikov approach and Lyapunov (Q- factorization) exponent were used to determine the threshold values for the chaotic behaviors in both the single and double well Duffing oscillators. The optimal values were obtained and the dynamical behaviors showed the intersection of manifold which were illustrated with MATHCAD software?s. Results obtained indicated that the behaviors of the perturbed Duffing oscillator were chaotic and highly unstable with repeated resonances of successively high periods. As a consequence, the functions with symmetric wells were separated by the barriers at periodic points and the perturbed systems produced three equilibria points which showed similarities in behaviors. Furthermore, the method of Lyapunov exponent narrowed the range of the critical threshold values and detected mutations in the chaotic systems. Numerical simulations showed that as the parameters were varied, repeated resonances of successively high periods occurred leading to unstable chaotic behaviors both for single and double well except for excited systems with positive linear stiffness. Keywords: Chaos, Single well oscillator, Double well oscillator, Excitation.

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