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

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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.

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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.

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Correspondence to Bocheng Bao.

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

Appendix

Appendix

To be helpful for more readers, the MATLAB program code for calculating the local basin of attraction in Fig. 5a is appended in Fig. 12.

Fig. 12
figure 12figure 12

MATLAB program code a sub-program code (mHNN_2N.m) b main-program code (main_program.m)

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Chen, C., Chen, J., Bao, H. et al. Coexisting multi-stable patterns in memristor synapse-coupled Hopfield neural network with two neurons. Nonlinear Dyn 95, 3385–3399 (2019). https://doi.org/10.1007/s11071-019-04762-8

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  • DOI: https://doi.org/10.1007/s11071-019-04762-8

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