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Energy flow-guided synchronization between chaotic circuits

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  • Yao, Zhao
  • Zhou, Ping
  • Alsaedi, Ahmed
  • Ma, Jun

Abstract

A variety of nonlinear electric devices are suitable for building chaotic circuits by setting appropriate values for parameters in the linear and nonlinear electronic components. The capacitor and induction coil can contain time-varying physical field energy when the time-varying current passed across these devices. When the outputs end of two chaotic circuits are connected via certain coupling devices, energy flow can be propagated bidirectionally and complete synchronization is reached when the energy pumping from the outputs end is balanced. In this paper, a nonreversing diode is connected into the coupling channel to adjust the energy flow via the coupling components (resistor, capacitor, induction coil), which connects the outputs end of two Chua circuits (in chaotic or periodical states). According to Helmholtz’ theorem, the Hamilton energy of the dimensionless chaotic systems under unidirectional coupling is calculated. When the two coupled Chua systems are selected with different initial values, they contain different initial field energies because the Hamilton energy is dependent on the variables of this system completely. When energy flow is propagated and pumped along the coupling channel, synchronization can be realized. Otherwise, synchronization approach is blocked even the coupling intensity is increased greatly. In this work, a single coupling channel connecting a nonreversing diode and resistor (capacitor, induction coil, respectively) in series is built to explore synchronization approach. The results show that the synchronization realization is dependent on the coupling devices and circuit verification is also supplied. It gives important clues to understand the synchronization mechanism in a forward neural network.

Suggested Citation

  • Yao, Zhao & Zhou, Ping & Alsaedi, Ahmed & Ma, Jun, 2020. "Energy flow-guided synchronization between chaotic circuits," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    • Handle: RePEc:eee:apmaco:v:374:y:2020:i:c:s0096300319309907
    DOI: 10.1016/j.amc.2019.124998
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