Nonlinear Dynamics

, Volume 90, Issue 4, pp 2359–2369 | Cite as

Numerical analyses and experimental validations of coexisting multiple attractors in Hopfield neural network

  • Bocheng Bao
  • Hui Qian
  • Jiang Wang
  • Quan Xu
  • Mo Chen
  • Huagan Wu
  • Yajuan Yu
Original Paper
First Online:
Received:
Accepted:

Abstract

By simplifying connection topology of Hopfield neural network (HNN) with three neurons, a kind of HNN-based nonlinear system is proposed. Taking a coupling-connection weight as unique adjusting parameter and utilizing conventional dynamical analysis methods, dynamical behaviors with the variation of the adjusting parameter are discussed and coexisting multiple attractors’ behavior under different state initial values are investigated. The results imply that the HNN-based system displays point, periodic, and chaotic behaviors as well as period-doubling and tangent bifurcation routes; particularly, this system exhibits some striking phenomena of coexisting multiple attractors, such as, a pair of single-scroll chaotic attractors accompanied with a pair of periodic attractors, a pair of periodic attractors with two periodicities, and so on. Of particular interest, it should be highly significant that a hardware circuit of the HNN-based system is developed by using commercially available electronic components and many kinds of coexisting multiple attractors are captured from the hardware experiments. The results of the experimental measurements have well consistency to those of MATLAB and PSpice simulations.

Keywords

Hopfield neural network (HNN)-based system Coexisting multiple attractors State initial value Hardware experiment 
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Notes

Acknowledgements

This work was supported by the grants from the National Natural Science Foundations of China under Grant Nos. 51777016, 61705021, 61601062, 11602035, and 51607013.

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.School of Information Science and EngineeringChangzhou UniversityChangzhouChina
  2. 2.School of Mathematics and PhysicsChangzhou UniversityChangzhouChina

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