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Coexisting multi-stable patterns in memristor synapse-coupled Hopfield neural network with two neurons

  • Chengjie Chen
  • Jingqi Chen
  • Han Bao
  • Mo Chen
  • Bocheng BaoEmail author
Original Paper
  • 73 Downloads

Abstract

When possessing a potential difference between two neurons, an electromagnetic induction current appears in the Hopfield neural network (HNN), which can be emulated by a flux-controlled memristor synapse. Thus, a three-order two-neuron-based autonomous memristive HNN is presented in this paper, which is the lowest order and has not been reported in the previous studies. With the mathematical model, the detailed stability analyses for the line equilibrium are executed, so that the fold and Hopf bifurcation sets and stability region distributions in the parameter plane are obtained. Furthermore, numerical results of coexisting bifurcation patterns are investigated, which are confirmed effectively by local basins of attraction and phase plane plots. The numerical results demonstrate coexisting multi-stable patterns of the spiral chaotic patterns with different dynamic amplitudes, periodic patterns with different periodicities, and stable resting patterns with different positions in the memristive HNN. Besides, the circuit synthesis and breadboard experiments are performed to well validate the numerical simulations.

Keywords

Hopfield neural network (HNN) Memristor synapse Coexisting multi-stable patterns Line equilibrium Circuit synthesis 

Notes

Acknowledgements

This work was supported by the grants from the National Natural Science Foundations of China under 51777016, 61601062, 61801054, and 11602035, and the Natural Science Foundations of Jiangsu Province, China under BK20160282.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest. These authors contribute equally to this work.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Information Science and EngineeringChangzhou UniversityChangzhouChina
  2. 2.College of Automation EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina

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