https://doi.org/10.1140/epjp/s13360-024-05038-w
Regular Article
Transition to extreme events in a coupled memristive Hindmarsh–Rose neuron system
1
Centre for Nonlinear Systems, Chennai Institute of Technology, 600069, Chennai, Tamilnadu, India
2
Centre for Computational Modeling, Chennai Institute of Technology, 600069, Chennai, Tamilnadu, India
3
Department of Physics, Jamal Mohamed College, 620020, Tiruchirappalli, Tamilnadu, India
Received:
9
October
2023
Accepted:
24
February
2024
Published online:
11
March
2024
The sharing of action potentials between the brain cells allows for communication between them. The improper transfer of these action potentials between them may probably be the cause of many neuronal diseases. In an earlier work, we tried to simulate the neurons by a Hindmarsh–Rose neuron model employing an active flux-controlled memristor wherein we had reported the superextreme spiking and multistability observed in the system. This work is a continuation of same. We name the neuron model, as the memristive Hindmarsh–Rose neuron model (MHRN) and have studied its individual dynamics from a different perspective by having the active flux-controlled memristor to take into account the electromagnetic inductance acting on the neurons. We have also studied the collective dynamics of the two-coupled MHRN model using unidirectional and bidirectional coupling schemes. We have found that as the strength of the coupling, which can be taken as the strength of synaptic interchange, is varied, the coupled system showed varied behaviors, such as desynchronization and complete synchronization states. Our studies reveal the large amplitude excursions of the system variables from their mean values upon proper choice of parameters. These large amplitude excursions are what are known in nonlinear theory as extreme events. Also, we have observed transient extreme events in the system. We have tried to explain neuronal activity such as bursting and spiking of the neurons as arising due to extreme events and their absence as non-extreme events. We have constructed basins of attraction, phase portraits for the individual and coupled systems, set up threshold laws to identify the extreme events, calculated probability distribution function and two parameter phase diagrams for confirming the same.
S. Dinesh Vijay and K. Thamilmaran have equally contributed to this work.
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 Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. 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.
