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Dynamics, synchronization and analog circuit implementation of a discrete neuron-like map with pulsating spiral dynamics

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  • Zhu, Wanting
  • Sun, Kehui
  • Wang, Huihai
  • Fu, Longxiang
  • Minati, Ludovico

Abstract

Owing to their computational efficiency and generative potential, discrete neural models have been gaining interest, both theoretically and towards engineering applications. In this paper, we propose a discrete map endowed with neuron-like dynamics and two distinguishing properties. Namely, the attractor has a spiral topology, and it has a cavity. The size of this cavity shows a non-monotonic relationship to a control parameter, delineating a pulsating behavior. The map shows a multitude of qualitatively-different periodic, chaotic, and hyperchaotic behaviors as a function of the control parameter settings, and its jump points restrict the internal and external size of the attractor. The oscillation frequency is also controllable and also shows a non-monotonic effect. In preparation for future work realizing neural-like networks, we demonstrate the synchronizability by coupling two nodes through a quadratic discrete memristor as the synapse. Finally, the analog circuit realizing this map is implemented and its dynamics are studied experimentally via a comprehensive set of measurements. As the control parameter is varied, the dynamic contraction and expansion of the attractor are observed alongside its well-developed spiral structure.

Suggested Citation

  • Zhu, Wanting & Sun, Kehui & Wang, Huihai & Fu, Longxiang & Minati, Ludovico, 2024. "Dynamics, synchronization and analog circuit implementation of a discrete neuron-like map with pulsating spiral dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924008336
    DOI: 10.1016/j.chaos.2024.115281
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    References listed on IDEAS

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    1. Zhu, Wanting & Sun, Kehui & He, Shaobo & Wang, Huihai & Liu, Wenhao, 2023. "A class of m-dimension grid multi-cavity hyperchaotic maps and its application," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Xu, Ying & Jia, Ya & Ma, Jun & Alsaedi, Ahmed & Ahmad, Bashir, 2017. "Synchronization between neurons coupled by memristor," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 435-442.
    3. Lai, Qiang & Yang, Liang, 2023. "Discrete memristor applied to construct neural networks with homogeneous and heterogeneous coexisting attractors," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
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