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Coupling dynamics and synchronization mode in driven FitzHugh–Nagumo neurons

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  • Bosco, Nivea D.
  • Manchein, Cesar
  • Rech, Paulo C.

Abstract

We introduce a novel four-dimensional continuous-time nonautonomous dynamical system formed by coupling two sinusoidally driven FitzHugh–Nagumo (FHN) neurons. The study investigates dynamical behaviors and synchronization properties under three distinct scenarios: (i) coupling two identical chaotic systems, (ii) coupling a periodic system with a chaotic system, and (iii) coupling two identical periodic systems. Synchronization is analyzed in detail for the first two scenarios. In case (i), coupling suppresses chaotic behavior, inducing periodic dynamics characterized by intricate discontinuous spirals and self-similar shrimp-shaped periodic structures. Case (ii) reveals shrimp-shaped periodic structures and regions of coexisting attractors, showcasing the multistability inherent in nonlinear systems. For these two scenarios, we explore the transition from asynchronous states to intermittent and nearly synchronized states, driven by increasing coupling strength. The emergence of synchronization is interpreted in terms of the interaction between individual neuron dynamics and coupling. In case (iii), coupling completely stabilizes periodic dynamics, leading to an uniform periodic regime without chaotic behavior. Across all scenarios, increasing coupling strength in nonautononous FHN neuron models induces a transition from eventual finite-time synchronization events to stable coupling-driven synchronized states. We also demonstrate that, for two-coupled nonautonomous FHN neurons, the individual dynamics play a less significant role in the synchronization process compared to previous findings in coupled autonomous neuron models. This work highlights the complex interplay of coupling and intrinsic individual nonautonomous FHN neuron dynamics.

Suggested Citation

  • Bosco, Nivea D. & Manchein, Cesar & Rech, Paulo C., 2025. "Coupling dynamics and synchronization mode in driven FitzHugh–Nagumo neurons," Chaos, Solitons & Fractals, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:chsofr:v:193:y:2025:i:c:s0960077925001237
    DOI: 10.1016/j.chaos.2025.116110
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    References listed on IDEAS

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    1. Hu, Dongpo & Ma, Linyi & Song, Zigen & Zheng, Zhaowen & Cheng, Lifang & Liu, Ming, 2024. "Multiple bifurcations of a time-delayed coupled FitzHugh–Rinzel neuron system with chemical and electrical couplings," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    2. Sahu, S.R. & Raw, S.N., 2023. "Appearance of chaos and bi-stability in a fear induced delayed predator–prey system: A mathematical modeling study," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    3. Zhang, Yan & Qiao, Yuanhua & Duan, Lijuan & Miao, Jun, 2023. "Multistability of almost periodic solution for Clifford-valued Cohen–Grossberg neural networks with mixed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    4. Rech, Paulo C., 2022. "Self-excited and hidden attractors in a multistable jerk system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    5. Nathan S. Nicolau & Tulio M. Oliveira & Anderson Hoff & Holokx A. Albuquerque & Cesar Manchein, 2019. "Tracking multistability in the parameter space of a Chua’s circuit model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(5), pages 1-8, May.
    6. Lu, Lulu & Ge, Mengyan & Xu, Ying & Jia, Ya, 2019. "Phase synchronization and mode transition induced by multiple time delays and noises in coupled FitzHugh–Nagumo model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    7. Cheng, Haihui & Meng, Xinzhu & Hayat, Tasawar & Hobiny, Aatef, 2023. "Multistability and bifurcation analysis for a three-strategy game system with public goods feedback and discrete delays," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    8. Vinícius Wiggers & Paulo C. Rech, 2022. "On the dynamics of a Van der Pol–Duffing snap system," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(2), pages 1-6, February.
    9. Yu, Dong & Lu, Lulu & Wang, Guowei & Yang, Lijian & Jia, Ya, 2021. "Synchronization mode transition induced by bounded noise in multiple time-delays coupled FitzHugh–Nagumo model," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    10. Hu, Xueyan & Ding, Qianming & Wu, Yong & Huang, Weifang & Yang, Lijian & Jia, Ya, 2024. "Dynamical rewiring promotes synchronization in memristive FitzHugh-Nagumo neuronal networks," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    11. Cambraia, E.B.S.A. & Flauzino, J.V.V. & Prado, T.L. & Lopes, S.R., 2023. "Dependence on the local dynamics of a network phase synchronization process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).
    12. Singh, Jay Prakash, 2024. "A set of five generalised memristive synapses for the hidden nonlinear dynamics in three coupled neurons," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    13. Carlos F. da Silva & Paulo C. Rech, 2023. "Chaos suppression, hyperchaos, period-adding, and discontinuous spirals in a bidirectional coupling of Lorenz systems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(1), pages 1-7, January.
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