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Simplest transistor-based chaotic circuit with extreme events: Statistical characterization, synchronization, and analogy with interictal spikes

Author

Listed:
  • Kamdjeu Kengne, Léandre
  • Folifack Signing, Vitrice Ruben
  • Rossi Sebastiano, Davide
  • Wafo Tekam, Raoul Blaise
  • Ngamsa Tegnitsap, Joakim Vianney
  • Zhao, Manyu
  • Bao, Qingshi
  • Kengne, Jacques
  • Valdes-Sosa, Pedro Antonio
  • Minati, Ludovico

Abstract

This paper investigates the simplest autonomous chaotic circuit capable of generating extreme events, comprising a DC voltage source, a series resistor, a capacitor, three inductors, and two bipolar transistors. The statistical properties and synchronization of the extreme events generated by the system are characterized using a simplified equation model, realistic SPICE simulations, and experimental circuit measurements. Heavy-tailed amplitude distributions and Poisson-like inter-event intervals are uncovered, confirming the existence and uncorrelated nature of the extreme events generated in this elementary circuit. Furthermore, a regime is identified where the extreme events synchronize significantly more strongly than the underlying lower-amplitude continuous activity that paces the dynamics, and a novel approach to visualize this situation is introduced. By drawing a tentative parallel with the interictal spikes observed in the neuroelectrical recordings of epilepsy patients, the study proposes that the analog chaotic circuit under consideration could, in the future, serve as a physical model for studying epileptic-like dynamics in electronic networks.

Suggested Citation

  • Kamdjeu Kengne, Léandre & Folifack Signing, Vitrice Ruben & Rossi Sebastiano, Davide & Wafo Tekam, Raoul Blaise & Ngamsa Tegnitsap, Joakim Vianney & Zhao, Manyu & Bao, Qingshi & Kengne, Jacques & Vald, 2025. "Simplest transistor-based chaotic circuit with extreme events: Statistical characterization, synchronization, and analogy with interictal spikes," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924014462
    DOI: 10.1016/j.chaos.2024.115894
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    References listed on IDEAS

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    1. Thamilmaran, K. & Bhagyaraj, T. & Sabarathinam, S., 2024. "Extreme events in a damped Korteweg–de Vries (KdV) autonomous system: A comprehensive analysis," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    2. M. Ghil & Pascal Yiou & Stéphane Hallegatte & B. D. Malamud & P. Naveau & A. Soloviev & P. Friederichs & V. Keilis-Borok & D. Kondrashov & V. Kossobokov & O. Mestre & C. Nicolis & H. W. Rust & P. Sheb, 2011. "Extreme events: dynamics, statistics and prediction," Post-Print hal-00716514, HAL.
    3. repec:plo:pcbi00:1006186 is not listed on IDEAS
    4. Minati, Ludovico & Bartels, Jim & Li, Chao & Frasca, Mattia & Ito, Hiroyuki, 2022. "Synchronization phenomena in dual-transistor spiking oscillators realized experimentally towards physical reservoirs," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    5. Manivelan, S.V. & Sabarathinam, S. & Thamilmaran, K. & Manimehan, I., 2024. "Dynamical instabilities cause extreme events in a theoretical Brusselator model," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    6. Wafo Tekam, Raoul Blaise & Kengne, Jacques & Djuidje Kenmoe, Germaine, 2019. "High frequency Colpitts’ oscillator: A simple configuration for chaos generation," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 351-360.
    7. Reto Schneider, 2023. "Extreme events require new forms of financial collaboration to become more resilient," Environment Systems and Decisions, Springer, vol. 43(4), pages 544-554, December.
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