https://doi.org/10.1140/epjp/s13360-025-06568-7
Regular Article
Dynamics of small-world memristive neuronal networks: synchronization and extreme events in the Hindmarsh–Rose model
1
Centre for Nonlinear and Complex Networks, SRM Institute of Science and Technology, 600 089, Ramapuram, Chennai, Tamil Nadu, India
2
Center for Nonlinear and Complex Networks, SRM TRP Engineering College, 621 105, Tiruchirappalli, Tamil Nadu, India
3
Center for Research, Easwari Engineering College, 600 089, Chennai, Tamil Nadu, India
4
Center for Cognitive Science, Trichy SRM Medical College Hospital and Research Center, 621105, Tiruchirappalli, Tamil Nadu, India
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Received:
28
March
2025
Accepted:
19
June
2025
Published online:
5
July
2025
We investigate the dynamics of a diffusively coupled memristive Hindmarsh–Rose neuron models, where one neuron is subjected to noise while the other neuron is without noise. To begin with, we study the dynamics of uncoupled neurons, and it exhibits extreme and superextreme events, both with and without noise. These events occur in a completely uncoordinated with time. Furthermore, as the coupling strength between the two neurons gradually increases, the coupled neurons become completely synchronized in higher value of coupling strength, indicating complete mutual coordination. We provide numerical evidence through time-series plots spanning a time of 
, along with the threshold and its corresponding probability distributions. Moreover, the synchronized behavior of network of diffusively coupled memristive Hindmarsh–Rose was studied in different network topologies by the spatiotemporal and snapshot plots.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and 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.
