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Energy balance between two thermosensitive circuits under field coupling

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Abstract

A thermistor is connected to the induction coil in series of the Chua circuit and a thermosensitive oscillator is obtained by applying scale transformation on the physical variables and parameters in the circuit equations. The dynamics dependence on temperature and synchronization stability under field coupling are discussed in detail. The sole Hamilton energy for each thermosensitive oscillator is calculated, and energy pumping along the coupling channel is continued before reaching complete synchronization between two thermosensitive circuits. The energy propagation in the coupling channel is controlled by the physical property of electric components such as capacitor and inductor. The magnetic field energy (or electric field energy) is pumped across the coupling channel when induction coil (or capacitor) is used to activate field coupling between chaotic circuits. Within this work, capacitor, and induction coil are respectively used to synchronize two thermosensitive circuits and the energy balance is also controlled. When two identical thermosensitive oscillators are controlled adaptively to reach complete synchronization, the energy balance is also realized. Furthermore, the temperature parameter is changed to detect the synchronization stability, and energy pumping along the coupling components in the coupling channel is estimated for detecting complete synchronization approach. Analog circuit implement is verified via Multisim and synchronization realization is detected as well. The advantage of this coupling scheme is that energy is pumped rather than consuming the Joule heat in the coupling channel before reaching complete synchronization, and the coupling channel can also be controlled by external physical field. The involvement of thermistor makes the chaotic systems become sensitive to the temperature, while the coupling scheme still works well and energy balance is controlled for reaching complete synchronization. Finally, a section for exploring open problems is supplied to guide the realization of adaptive synchronization control and energy balance for other nonlinear systems and neural circuits.

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Acknowledgements

This project is supported by Gansu Natural Science Foundation under Grant No. 20JR5RA473. The authors thank Dr. Jun Ma for this checking and improvement in the writing.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Authors and Affiliations

  1. School of Science, Chongqing University of Posts and Telecommunications, Chongqing, 430065, China

    Ping Zhou, Xiufang Zhang & Xikui Hu

  2. Department of Physics, Lanzhou University of Technology, Lanzhou, 730050, China

    Xiufang Zhang & Guodong Ren

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  1. Ping Zhou
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  2. Xiufang Zhang
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Contributions

Xiufang Zhang and Xikui Hu validated the model approach and numerical results. Ping Zhou confirmed the experimental results, and edited the draft. Guodong Ren suggested this project, validated the proof and wrote this draft.

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Correspondence to Guodong Ren.

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Zhou, P., Zhang, X., Hu, X. et al. Energy balance between two thermosensitive circuits under field coupling. Nonlinear Dyn 110, 1879–1895 (2022). https://doi.org/10.1007/s11071-022-07669-z

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