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Infinite strange non-chaotic attractors in a non-autonomous jerk system

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Abstract

This research delves into the intricate relationship between two fascinating phenomena: megastability and strange non-chaotic attractors (SNAs). The study centers on a 4D jerk system that incorporates an additional periodic force, aiming to unravel the interplay between these phenomena and shed light on the underlying mechanisms. By manipulating a control parameter, the system's behavior reveals a spectrum of attractors, including the torus, strange non-chaotic attractors, and chaotic states. This diversity underscores the system’s complexity and responsiveness to parameter changes. To validate the observed megastability, the research employs rigorous analytical techniques. Phase portraits visually capture the system’s trajectories in its state space, while Poincaré sections reveal its periodic behavior. Basin of attraction analysis provides insights into the reliability of the observed megastable behavior. The study then delves into the transitions between these attractors. Bifurcation analysis identifies critical parameter values where the system’s dynamics change qualitatively, while Lyapunov exponents quantify the system's sensitivity to initial conditions. The presence and attributes of complex behavior of the system are confirmed through power spectrum analysis, the exploration of nearby point separations, and the identification of singular continuous spectrum patterns. In conclusion, this comprehensive investigation unveils the intricate fusion of complex behaviors within the 4D jerk system. The study's methodologies, ranging from validation to transition analysis and confirmation of these intricate properties, deepen our understanding of complex dynamical systems.

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Infinite strange non-chaotic attractors.

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Acknowledgements

This work is funded by the Center for Nonlinear Systems, Chennai Institute of Technology, India, vide funding number CIT/CNS/2023/RP/003.

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Authors and Affiliations

  1. Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai, 600069, Tamil Nadu, India

    Prasina Alexander & Karthikeyan Rajagopal

  2. Department of Electronics and Communication Engineering, Vemu Institute of Technology, Chithoor, India

    Balamurali Ramakrishnan & D. Chandrasekhar

  3. Department of Electronics and Communications Engineering, University Centre of Research and Development, Chandigarh University, Mohali, 140413, Punjab, India

    Karthikeyan Rajagopal

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  1. Prasina Alexander
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  3. D. Chandrasekhar
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  4. Karthikeyan Rajagopal
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Contributions

PA was involved in the conceptualization and development of the necessary simulations. BR was responsible for the dynamical analysis of the chaotic oscillator. DC was responsible for the preparation of the necessary tests for SNA. KR was responsible for the preparation of the original manuscript and also the verification and compiling of the results.

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Correspondence to Karthikeyan Rajagopal.

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Alexander, P., Ramakrishnan, B., Chandrasekhar, D. et al. Infinite strange non-chaotic attractors in a non-autonomous jerk system. Eur. Phys. J. B 96, 135 (2023). https://doi.org/10.1140/epjb/s10051-023-00603-1

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