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Resonance Oscillation and Transition to Chaos in \(\phi ^8\)-Duffing–Van der Pol Oscillator

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Abstract

In this paper, an exciting and interesting transition to chaos in a complex \(\phi ^8\)-DVP oscillator is studied. We first examine the stability conditions for the fixed points and then analyzed the resonance oscillation using the multiple scale method. The regions of chaotic and periodic behavior which leads to multi-stability of attractors and changes in the geometry of the attractors via bifurcation parameter \((\gamma )\), the driving force (f) and its frequency \((\omega )\)—a phenomenon of chaotification were further obtained. Our analytical predictions confirm the numerical results in which the model exhibits imbricated period-doubling, Hopf bifurcation, intermittent bifurcation, sudden chaos, unstable states, and hidden dynamics. We explore the chaotic behavior of the new model using the indicators, namely bifurcation diagrams, Lyapunov exponents, Poincáre cross-sections, phase portraits and time series for better visualization and characterization. Finally, the circuit realization of the proposed model is designed using MultiSIM software and hardware components.

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Acknowledgements

The ideas of and contributions from A.N. Njah, O.I. Olusola and U.E. Vincent are gratefully acknowledged. I also thank the anonymous referees for their constructive and helpful suggestions.

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This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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  1. Department of Physics, Federal University of Technology, Akure, Ondo State, Nigeria

    A. O. Adelakun

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Adelakun, A.O. Resonance Oscillation and Transition to Chaos in \(\phi ^8\)-Duffing–Van der Pol Oscillator. Int. J. Appl. Comput. Math 7, 82 (2021). https://doi.org/10.1007/s40819-021-01005-6

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