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Simplest symmetric chaotic flows: the strange case of asymmetry in Master Stability Function

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Abstract

In this research, we investigate the existence of symmetry in the simplest three-dimensional chaotic flows with unique features. We search the simplest Sprott chaotic systems, systems with no equilibrium, stable equilibrium, and systems with the line, curve, and surface equilibrium. We show that some of such systems are symmetric systems. Also, only a few have coexisting symmetric attractors. Moreover, we study the synchronization of these symmetric systems to understand the collective behavior of the network of such systems. We compute the Master Stability Function, which provides a necessary condition for synchronization. We consider the linear coupling function in different one-component schemes. It is observed that the synchronization in these systems, has no relation with the coupling of symmetric variables. Furthermore, the results show that the attractors may have different Master Stability Functions for the systems with coexisting symmetric attractors.

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Data Availability Statement

My manuscript has no associated data or the data will not be deposited.

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Acknowledgements

Karthikeyan Rajagopal has been partially funded by the Research grant of Center for Nonlinear Systems, Chennai Institute of Technology with reference number CIT/CNS/2021/RP-017.

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Authors and Affiliations

  1. Center for Nonlinear Systems, Computational Biology of Technology, Chennai, India

    Karthikeyan Rajagopal

  2. Health Technology Research Institute, Amirkabir University of Technology, 424 Hafez Ave., 15875-4413, Tehran, Iran

    Ali Jafari

  3. School of Physics and Electronics, Central South University, Changsha, 410083, China

    Shaobo He

  4. Department of Biomedical Engineering, Amirkabir University of Technology, 424 Hafez Ave., 15875-4413, Tehran, Iran

    Fatemeh Parastesh

  5. Center for Computational Biology, Chennai Institute of Technology, Chennai, India

    Sajad Jafari

  6. Department of Mathematics, Statistics and Physics, Qatar University, Doha, 2713, Qatar

    Iqtadar Hussain

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  1. Karthikeyan Rajagopal
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  2. Ali Jafari
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  3. Shaobo He
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  4. Fatemeh Parastesh
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Correspondence to Sajad Jafari.

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Rajagopal, K., Jafari, A., He, S. et al. Simplest symmetric chaotic flows: the strange case of asymmetry in Master Stability Function. Eur. Phys. J. Spec. Top. 230, 1999–2010 (2021). https://doi.org/10.1140/epjs/s11734-021-00131-y

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  • DOI: https://doi.org/10.1140/epjs/s11734-021-00131-y

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