https://doi.org/10.1140/epjs/s11734-025-01666-0
Regular Article
Chaotic dynamics and synchronization control of a memristive FitzHugh–Rinzel oscillator
1
School of Mathematics and Computer Science, Yan’an University, No. 1 Gongxue North Road, 716000, Yan’an, Shaanxi, People’s Republic of China
2
School of Architecture and Civil Engineering, Yan’an University, No. 1 Gongxue North Road, 716000, Yan’an, Shaanxi, People’s Republic of China
Received:
24
February
2025
Accepted:
26
April
2025
Published online:
12
May
2025
This paper introduces a novel memristive FitzHugh–Rinzel neural oscillator and investigates its chaotic dynamics using bifurcation diagrams and Lyapunov exponents. A neural network based on this oscillator is constructed to study synchronization control under a non-local coupling structure, considering electrical, chemical, and electrochemical coupling. The results show that synchronization occurs at weaker coupling strengths under chemical coupling than electrical coupling, with a non-monotonic decrease in synchronization error as the coupling strength increases. However, at high chemical and electrochemical coupling strengths, the system undergoes oscillation death, where neurons cease oscillating and reach a stable state. These findings highlight the distinct roles of chemical and electrochemical interactions in shaping neural network synchronization and collective dynamics.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
