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Multiple attractors and strange nonchaotic dynamical behavior in a periodically forced system

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Abstract

This work investigates the dynamical behaviors of the third-order chaotic oscillator with threshold controller as its nonlinear element. The system reveals several complex dynamics with the presence and absence of external excitation. For a specific set of control parameter values, the system exhibits three different routes, which include the regular period-doubling route, period-3 doubling to chaos, and three tori to chaos are realized with the aid of bifurcation and Lyapunov exponents. In particular, by tuning the values of the parameters, the coexistence of multiple attractors is also revealed. More interestingly, we uncovered strange nonchaotic attractors (SNA) in a single periodically forced system through an intermittency route. The presence of SNA behaviors is calculated by using several characterizing quantities such as Lyapunov exponent, Poincarè section, singular-continuous spectrum analysis, and 0–1 test analysis. The performance of the system is investigated using the fixed-point analysis, numerical integration of mathematical model, and real-time experimental results.

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Acknowledgements

This research work is supported by SERB under project No: SR/S2/HEP-042/2012 and authors thank them for providing financial support. The authors like to thank Dr. K. Murali Anna University, Chennai for his valuable suggestion. A. Chithra acknowledges Dr. K. Srinivasan and Dr. K. Suresh from Center for Nonlinear Dynamics (CNLD), Tiruchirappalli, for helpful discussions.

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  1. Department of Physics, B.S Abdur Rahman Crescent Institute of Science and Technology, Chennai, India

    A. Chithra & I. Raja Mohamed

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  1. A. Chithra
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Chithra, A., Raja Mohamed, I. Multiple attractors and strange nonchaotic dynamical behavior in a periodically forced system. Nonlinear Dyn 105, 3615–3635 (2021). https://doi.org/10.1007/s11071-021-06608-8

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