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Super extreme events and dragon kings in a memristive coupled Rulkov maps

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Abstract

Unforeseeable rare events, referred to as extreme events (EEs), can occur in various real-world contexts. When comparing EEs, the super EEs and dragon kings are the most harmful and occur occasionally in both natural and artificial systems. In this study, we consider a discrete system of Rulkov maps coupled via a tangential form of the memristive function to investigate the existence of both super EEs and dragon king events. Primarily, bifurcation analysis and Lyapunov exponents demonstrate that the transition to hyper-chaos occurs when the control parameter is increased to larger values. Following that, we analyze the appearance of super EEs by setting the parameter in the region of hyper-chaos, and we perform the critical amplitude threshold and probability density function to illustrate such occurrences. Furthermore, we use statistical characterizations such as the complementary cumulative distribution function (CCDF) and the DK test to delineate the emergence of the dragon kings. Finally, we perform a two-parameter analysis to acquire a complete picture of the occurrence of the observed events.

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The authors confirm that the data supporting the findings of this study are available within the article.

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Acknowledgements

DP is partially supported by National Natural Science Foundation of china (NSFC) No. 12375031. We gratefully acknowledge this work is funded by the Center for Nonlinear Systems, Chennai Institute of Technology (CIT), India, vide funding number CIT/CNS/2024/RP-005.

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Authors and Affiliations

  1. Institute of Systems Science, Huaqiao University, Xiamen, 361021, China

    Premraj Durairaj

  2. College of Information Science and Engineering, Huaqiao University, Xiamen, 361021, China

    Premraj Durairaj

  3. College of Mechanical Engineering and Automation, Huaqiao University, Xiamen, 361021, China

    Premraj Durairaj

  4. Center for Nonlinear Systems, Chennai Institute of Technology, Chennai, 600069, Tamilnadu, India

    Premraj Durairaj, Sathiyadevi Kanagaraj & Karthikeyan Rajagopal

  5. Department of Electronics and Communication Engineering, Vemu Institute of Technology, Chitoor, 517112, Andhra Pradesh, India

    Anitha Karthikeyan

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  1. Premraj Durairaj
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  4. Karthikeyan Rajagopal
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Correspondence to Karthikeyan Rajagopal.

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Durairaj, P., Kanagaraj, S., Karthikeyan, A. et al. Super extreme events and dragon kings in a memristive coupled Rulkov maps. Eur. Phys. J. Spec. Top. (2024). https://doi.org/10.1140/epjs/s11734-024-01166-7

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