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Various coexisting attractors, asymmetry analysis and multistability control in a 3D memristive jerk system

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Abstract

In this paper, the dynamics of a 3D memristive jerk oscillator is investigated both analytically and numerically with the help of Routh-Hurwitz criteria, phase portraits, bifurcation diagrams, and basins of attraction. The analyses show that the system is bistable because of its inversion symmetry. In addition, the system enters chaos by period-doubling bifurcation. It has a double-scroll chaotic attractor (as a result of mixing two bistable chaotic attractors). More interestingly, multistability involving the coexistence of multiple stable states (i.e., four and up to six coexisting attractors) is found when monitoring the system parameters and initial conditions. Furthermore, the state control from multistability to monostability is performed using the linear augmentation scheme. We also address the realistic issue of symmetry-breaking by considering an asymmetric memristive device. The asymmetry analysis produces two asymmetric coexisting bifurcation diagrams (i.e., asymmetric bi-stability) each of which exhibits its own sequence of bifurcations to chaos when monitoring the main control parameter. The PSpice circuit simulation results match well with the theoretical and numerical results. Finally, the microcontroller-based experimental implementation is carried out to verify the analytical and numerical studies. To the best of our knowledge, we would like to stress that the results obtained in this paper are unique and of great importance for developing and the understanding of memristive devices-based systems.

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Acknowledgements

This work was conducted as part of the research scholarship “Ernst Mach Grant, worldwide” financed by the “Federal Ministry of Education, Science and Research (BMBWF)” and the awarding organization “Austrian Agency for International Cooperation in Education and Research (OeAD-GmbH), Mobility Programs, Bilateral and Multilateral Cooperation (MPC)”. Léandre Kamdjeu would like to thank Prof. Fotsin Hilaire. B., Prof. Mboupda Pone Justin R., Prof. Pelap François B., and Prof. Kengne Jacques (all from the University of Dschang, Cameroon) for their recommendation in this research grant and for their valuable teaching. The authors would like to thank BOUI Bertrand for his help during the microcontroller-based implementation.

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Authors and Affiliations

  1. Research Unit of Condensed Matter, Electronics and Signal Processing, Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon

    Léandre Kamdjeu Kengne

  2. School of Computational and Mathematical Sciences, Massey University, Palmerston North, New Zealand

    Sishu Shankar Muni

  3. Institute for Smart- Systems Technologies, University of Klagenfurt, Klagenfurt, Austria

    Léandre Kamdjeu Kengne, Jean Chamberlain Chedjou & Kyamakya Kyandoghere

  4. Department of Physical Sciences, Indian Institute of Science and Educational Research Kolkata, Campus Road, Mohanpur, West Bengal, 741246, India

    Sishu Shankar Muni

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  1. Léandre Kamdjeu Kengne
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  2. Sishu Shankar Muni
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  3. Jean Chamberlain Chedjou
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  4. Kyamakya Kyandoghere
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Correspondence to Léandre Kamdjeu Kengne.

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Kengne, L.K., Muni, S.S., Chedjou, J.C. et al. Various coexisting attractors, asymmetry analysis and multistability control in a 3D memristive jerk system. Eur. Phys. J. Plus 137, 848 (2022). https://doi.org/10.1140/epjp/s13360-022-03073-z

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