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Synchronization and different patterns in a network of diffusively coupled elegant Wang–Zhang–Bao circuits

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Abstract

Synchronization in coupled oscillators is of high importance in secure communication and information processing. Due to this reason, a significant number of studies have been performed to investigate the synchronization state in coupled circuits. Diffusive coupling is the simplest connection between the oscillators, which can be implemented through a variable resistor between two variables of two circuits. The Chua’s circuit is the most famous chaotic circuit whose dynamics have been investigated in many studies. However, Wang–Zhang–Bao (WZB) is another chaotic circuit that can exhibit exciting behaviors such as bistability. Thus, this study aims to investigate the cooperative dynamics of the WZB circuit in its elegant parameter values. To this issue, first, we explored the dynamic behavior of the elegant WZB circuit using the bifurcation diagrams, the Lyapunov exponents, and the basins of attraction. Based on the results, we found the range of the bifurcation parameter and the initial conditions wherein the system is bistable. Subsequently, setting the parameters in the monostable region, we studied the synchronization state of two diffusively coupled WZB circuits analytically and numerically. Consequently, we used master stability functions and temporally averaged synchronization error as the analytical and numerical tools to explore the synchronization state. Then we numerically examined the synchronization state in a network of 100 nonlocally coupled WZB oscillators. As a result, we found imperfect chimera and phase synchronization in the studied network before getting synchronized.

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Acknowledgements

This work is funded by the Natural Science Foundation of Changzhou College of Information Technology, China, Grant No. CXZK202102Y; and the Design and Development of Intelligent Workshop Production Information Cloud Platform, CCIT, Grant No. KYPT202103G. This work is funded by the Design and Development of Intelligent Workshop Production Information Cloud Platform, CCIT, Grant No. KYPT202103G, Center for Nonlinear Systems, Chennai Institute of Technology, India vide funding number CIT/CNS/2022/RD/006. This work is supported by Al-mustaqbal university college.

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Authors and Affiliations

  1. School of Electronic Engineering, Changzhou College of Information Technology, Changzhou, 213164, China

    Rending Lu

  2. Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai, India

    Balamurali Ramakrishnan

  3. Building and Construction Engineering Technology Department, AL-Mustaqbal University College, Hillah, 51001, Iraq

    Mayadah W. Falah

  4. Computer Sciences, University of Technology, Al Sina’a Street, Baghdad, 10066, Iraq

    Alaa Kadhim Farhan

  5. Department of Applied Sciences, University of Technology, Baghdad, 10066, Iraq

    Nadia M. G. Al-Saidi

  6. Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Viet-Thanh Pham

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  1. Rending Lu
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Collective Behavior of Nonlinear Dynamical Oscillators. Guest editors: Sajad Jafari, Bocheng Bao, Christos Volos, Fahimeh Nazarimehr, Han Bao.

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Lu, R., Ramakrishnan, B., Falah, M.W. et al. Synchronization and different patterns in a network of diffusively coupled elegant Wang–Zhang–Bao circuits. Eur. Phys. J. Spec. Top. 231, 3987–3997 (2022). https://doi.org/10.1140/epjs/s11734-022-00690-8

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