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Messee Goulefack L, F Ramos M, Yamapi R, Anteneodo C. Collective dynamics of nonlocally coupled Hindmarsh-Rose neurons modified by magnetic flux. CHAOS (WOODBURY, N.Y.) 2023; 33:083124. [PMID: 37549126 DOI: 10.1063/5.0155683] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2023] [Accepted: 07/16/2023] [Indexed: 08/09/2023]
Abstract
We investigate the dynamics of nonlocally coupled Hindmarsh-Rose neurons, modified by coupling the induced magnetic flux to the membrane potential with a quadratic memristor of strength k. The nonlocal coupling consists of the interaction of each neuron with its neighbors within a fixed radius, which influence the membrane potential of the neuron with coupling intensity σ. For such local dynamics and network of interactions, we investigate how variations of k and σ affect the collective dynamics. We find that when increasing k as well as when increasing σ, coherence typically increases, except for small ranges of these parameters where the opposite behavior can occur. Besides affecting coherence, varying k also affects the pattern of bursts and spikes, namely, for large enough k, burst frequency is augmented, the number and amplitude of the spikes are reduced, and quiescent periods become longer. Results are displayed for an intermediate range of interactions with radius 1/4 of the network size, but we also varied the range of interactions, ranging from first-neighbor to all-to-all couplings, observing in all cases a qualitatively similar impact of induction.
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Affiliation(s)
- L Messee Goulefack
- Fundamental Physics Laboratory, Department of Physics, Faculty of Science, University of Douala, Box 24, 157 Douala, Cameroon
- Department of Physics, Pontifical Catholic University of Rio de Janeiro, Rua Marquês de São Vicente, 225-22451-900 Gávea, Rio de Janeiro, Brazil
| | - Marlon F Ramos
- Faculty of Technology, Rio de Janeiro State University (FAT UERJ), 27.537-000 Resende, Rio de Janeiro, Brazil
| | - R Yamapi
- Fundamental Physics Laboratory, Department of Physics, Faculty of Science, University of Douala, Box 24, 157 Douala, Cameroon
| | - C Anteneodo
- Department of Physics, Pontifical Catholic University of Rio de Janeiro, Rua Marquês de São Vicente, 225-22451-900 Gávea, Rio de Janeiro, Brazil
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Simo GR, Njougouo T, Aristides RP, Louodop P, Tchitnga R, Cerdeira HA. Chimera states in a neuronal network under the action of an electric field. Phys Rev E 2021; 103:062304. [PMID: 34271625 DOI: 10.1103/physreve.103.062304] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2020] [Accepted: 05/25/2021] [Indexed: 11/07/2022]
Abstract
The phenomenon of the chimera state symbolizes the coexistence of coherent and incoherent sections of a given population. This phenomenon identified in several physical and biological systems presents several variants, including the multichimera states and the traveling chimera state. Here, we numerically study the influence of a weak external electric field on the dynamics of a network of Hindmarsh-Rose (HR) neurons coupled locally by an electrical interaction and nonlocally by a chemical one. We first focus on the phenomena of traveling chimera states and multicluster oscillating breathers that appear in the electric field's absence. Then in the field's presence, we highlight the presence of a chimera state, a multichimera state, an alternating chimera state, and a multicluster traveling chimera.
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Affiliation(s)
- Gaël R Simo
- Research Unit Condensed Matter, Electronics and Signal Processing, Department of Physics, Faculty of Sciences, University of Dschang, P.O. Box 67, Dschang, Cameroon
| | - Thierry Njougouo
- Research Unit Condensed Matter, Electronics and Signal Processing, Department of Physics, Faculty of Sciences, University of Dschang, P.O. Box 67, Dschang, Cameroon
| | - R P Aristides
- São Paulo State University (UNESP), Instituto de Física Teórica, Rua Doutor Bento Teobaldo Ferraz 271, Bloco II, Barra Funda, 01140-070 São Paulo, Brazil
| | - Patrick Louodop
- Research Unit Condensed Matter, Electronics and Signal Processing, Department of Physics, Faculty of Sciences, University of Dschang, P.O. Box 67, Dschang, Cameroon
| | - Robert Tchitnga
- Research Unit Condensed Matter, Electronics and Signal Processing, Department of Physics, Faculty of Sciences, University of Dschang, P.O. Box 67, Dschang, Cameroon.,Institute of Surface Chemistry and Catalysis, University of Ulm, Albert-Einstein-Allee 47, 89081 Ulm, Germany
| | - Hilda A Cerdeira
- São Paulo State University (UNESP), Instituto de Física Teórica, Rua Doutor Bento Teobaldo Ferraz 271, Bloco II, Barra Funda, 01140-070 São Paulo, Brazil.,Epistemic, Gomez & Gomez Ltda. ME, Avenida Professor Lineu Prestes 2242, Cietec, Sala 244, 05508-000 São Paulo, Brazil
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