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Memristive-cyclic Hopfield neural network: spatial multi-scroll chaotic attractors and spatial initial-offset coexisting behaviors

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Abstract

Neural networks with changeable synaptic weights usually exhibit more complex and diverse dynamics than those with fixed synaptic weights. It was proved that the tri-neuron resistive-cyclic Hopfield neural network (RC-HNN) cannot show chaos. To this end, we first consider a RC-HNN with bipolar pulse current to generate double-scroll chaotic attractors. On this basis, we then construct a tri-neuron memristive-cyclic Hopfield neural network (MC-HNN) by replacing the resistive weights with memristive ones, and spatial multi-scroll chaotic behaviors and spatial initial-offset coexisting behaviors are revealed therein using phase portrait, Poincaré map and basin of attraction. The results manifest that by setting the parameters related to the internal states of three memristors, the MC-HNN can not only generate spatial multi-scroll chaotic attractors (MSCAs) with different scroll numbers, but also produce spatial initial-offset coexisting attractors (IOCAs) with different attractor numbers. Besides, an FPGA hardware platform is developed and the spatial MSCAs and spatial IOCAs are displayed experimentally to confirm the numerical simulations.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

This work was supported by the National Natural Science Foundations of China under Grant No. 62201094, Grant No. 62271088, Grant No. 52277001, and Grant No. 12172066, the Scientific Research Foundation of Jiangsu Provincial Education Department, China, under Grant No. 22KJB510001, and the Postgraduate Research & Practice Innovation Program of Jiangsu Province, China, under Grant No. KYCX23_3175.

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Authors and Affiliations

  1. School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213159, China

    Han Bao, Zhuguan Chen, Mo Chen, Quan Xu & Bocheng Bao

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  1. Han Bao
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  2. Zhuguan Chen
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  3. Mo Chen
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Correspondence to Bocheng Bao.

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Bao, H., Chen, Z., Chen, M. et al. Memristive-cyclic Hopfield neural network: spatial multi-scroll chaotic attractors and spatial initial-offset coexisting behaviors. Nonlinear Dyn 111, 22535–22550 (2023). https://doi.org/10.1007/s11071-023-08993-8

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