https://doi.org/10.1140/epjp/s13360-023-04845-x
Regular Article
Hamilton energy variations in memristive Hindmarsh–Rose neurons under attractive and repulsive couplings
1
Centre for Nonlinear Systems, Chennai Institute of Technology, 600069, Chennai, Tamil Nadu, India
2
Department of Computer Technology Engineering, College of Information Technology, Imam Ja’afar Al-Sadiq University, Baghdad, Iraq
3
Neural Engineering Laboratory, Department of Biomedical Engineering, University of Neyshabur, Neyshabur, Iran
4
Department of Electronics and Communication Engineering, Vemu Institute of Technology, Chithoor, India
5
Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
6
Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
Received:
2
July
2023
Accepted:
27
December
2023
Published online:
6
February
2024
Studying the dynamics of neuronal networks via complex networks is becoming increasingly important among neuroscientists. The Hamiltonian systems approach is a beneficial tool for analyzing the dynamics of such networks. Hamiltonian energy is a physical concept that describes the overall energy of the network by giving an energy value to each node. This paper aims to study the influence of attractive and repulsive couplings on the network’s energy variation. To do so, a ring network of memristive Hindmarsh–Rose models is considered. A variety of couplings, including electrical, chemical, electrochemical, and field couplings, is examined. The findings show that energy balance occurs in attractive coupling; while, cluster synchronization is observed in repulsive coupling. In repulsive coupling, when the network is cluster synchronous, an increment in the firing rate results in a decrement in the energy peak. The maximum energy is attained when the network is quiescent in repulsive couplings.
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.
