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Energy flow controls synchronization in a network coupled with memristive synapses

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Abstract

External stimulus and noisy disturbance can inject energy into nonlinear systems, and the energy propagation between different branch circuits is regulated to control the oscillatory states completely. In this work, memristive synapse is activated under energy diversity and the energy flow is guided to control the coupling channels adaptively between Chua circuits (in presenting periodic and/or chaotic states). The field energy in each nonlinear circuit is described by an equivalent Hamilton energy function and adaptive mechanism for field coupling is explained. For identical Chaotic Chua circuits, complete synchronization is controlled under energy balance. Transient chaos occurs in the Chua systems when the memristive parameter for coupling channel is below a saturation value, and then chaos is suppressed to present synchronous oscillation with stronger coupling intensity. In a chain network composed of Chua circuits, local energy balance is helpful to develop regular spatial patterns. Applying distinct diversity for initials will induce large diversity in energy for all nodes, the memristive channel can increase its parameter for reaching a higher value beyond the threshold, and a higher synchronization factor is obtained. These results indicate that local energy balance controls the collective behaviors of nonlinear oscillators and energy flow can be guided to control the synchronization stability in the network.

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Data Availability Statement

The data used to support the findings of this study are available from the corresponding author upon request. This manuscript has associated data in a data repository. [Authors’ comment: Data used in this work are obtained numerically by using the fourth order Runge-Kutta algorithm.]

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Acknowledgements

This project is partially supported by National Natural Science Foundation of China under Grant No. (12072139). The authors thank Miss Ying Xie for the help with the numerical confirmation and figures edition.

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Authors and Affiliations

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

    Bo Hou, Guodong Ren & Jun Ma

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

    Ping Zhou & Jun Ma

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  1. Bo Hou
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Correspondence to Jun Ma.

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Hou, B., Zhou, P., Ren, G. et al. Energy flow controls synchronization in a network coupled with memristive synapses. Eur. Phys. J. Plus 138, 293 (2023). https://doi.org/10.1140/epjp/s13360-023-03900-x

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