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Hidden extreme multistability with hyperchaos and transient chaos in a Hopfield neural network affected by electromagnetic radiation

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Abstract

Biological nervous system function is closely related to its dynamical behaviors, and some dynamical phenomena observed in biological systems can be detected in the simplified neural models. In this paper, the chaotic dynamics in a three-neuron-based Hopfield neural network (HNN) with stimulation of electromagnetic radiation is investigated. The neural network is modeled by utilizing a flux-controlled memristor to describe the effects of electromagnetic field on neurons. The simple neural model affected by electromagnetic radiation does not contain any equilibrium points, but can induce coexisting infinitely many hidden attractors, such as hyperchaos, transient hyperchaos, period, quasi-period, chaos as well as transient chaos with different chaotic times. In particular, the dynamics of hidden extreme multistability with hyperchaos and transient chaos in the neural network highly depends on the system parameters and state initial values. The coexistence of multiple hidden attractors is revealed via applying a host of numerical analysis methods including phase plots, time sequence waveforms, bifurcation diagrams, Lyapunov exponents and attraction basins. Besides, a HNN-based circuit consisting of commercially available electronic elements is designed to verify the theoretical analysis. Hardware measurement and MULTISIM simulation results are basically consistent with MATLAB numerical simulation results.

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Acknowledgements

This work is supported by National Natural Science Foundation of China (No.61971185) and Open Fund Project of Key Laboratory in Hunan Universities (No. 18K010).

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Correspondence to Chunhua Wang.

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Lin, H., Wang, C. & Tan, Y. Hidden extreme multistability with hyperchaos and transient chaos in a Hopfield neural network affected by electromagnetic radiation. Nonlinear Dyn 99, 2369–2386 (2020). https://doi.org/10.1007/s11071-019-05408-5

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