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Methodology for studying magnetic field effects on chimera states in Hindmarsh-Rose neuronal networks. Covers traveling chimera, multicluster chimera, and multicluster chimera breather transformations under spatial magnetic field applications.
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| name | chimera-magnetic-field-neuronal |
| description | Methodology for studying magnetic field effects on chimera states in Hindmarsh-Rose neuronal networks. Covers traveling chimera, multicluster chimera, and multicluster chimera breather transformations under spatial magnetic field applications. |
| version | 1.0.0 |
| author | Hermes Agent |
| license | MIT |
| metadata | {"hermes":{"tags":["chimera-state","hindmarsh-rose","magnetic-field","neuronal-dynamics","synchronization","neural-network","brain-cells","collective-dynamics"],"category":"ai_collection","arxiv_id":"2607.07426","arxiv_url":"https://arxiv.org/abs/2607.07426","published":"2026-07-08","authors":["Gael R Simo","Carmel T lambu","Adamou Dang Koko","Patrick Louodop","Robert Tchitnga","Hilda A. Cerdeira"],"categories":["nlin.AO"],"trigger_words":["chimera state","magnetic field","hindmarsh-rose","neuronal network","traveling chimera","multicluster chimera","chimera breather","synchronization","coherence","incoherence","brain cells"]}} |
| created | 2026-07-12 |
| updated | 2026-07-12 |
arXiv: 2607.07426 | Published: 2026-07-08 | Authors: Gael R Simo, Carmel T lambu, Adamou Dang Koko, Patrick Louodop, Robert Tchitnga, Hilda A. Cerdeira
This study demonstrates the influence of magnetic fields on three categories of chimera states in Hindmarsh-Rose (HR) neuronal networks:
The key discovery: magnetic fields can transform areas of incoherence into areas of coherence, enriching the synchronization field and providing insights into how magnetic fields affect brain cells.
A chimera state is a dynamical pattern in a network of identical oscillators where coherent (synchronized) and incoherent (desynchronized) domains coexist. In neuronal networks, this corresponds to some brain regions showing synchronized activity while others remain chaotic.
The study applies magnetic fields in three spatial configurations:
The HR model describes neuronal spiking-bursting dynamics:
dx/dt = y - ax³ + bx² - z + I_ext
dy/dt = c - dx² - y
dz/dt = ε(s(x - x₀) - z) + ε·B(t)
Where:
The local order parameter measures synchronization:
r_i = |(1/δ) Σ_{j=i-δ/2}^{i+δ/2} exp(i·θ_j)|
where θ_j is the phase of neuron j, and δ is the neighborhood size.
| Initial State | Magnetic Field Applied | Resulting Phenomenon |
|---|---|---|
| Traveling chimera | Full network | Modified traveling pattern |
| Traveling chimera | Half network | Boundary shift, new coherence zones |
| Multicluster chimera | Full network | Cluster restructuring |
| Multicluster chimera breather | Dual regions | Multialternating chimera state |
| Any chimera | Spatial field | Multitraveling chimera state |
The magnetic field acts as a control parameter that:
Understanding how magnetic fields affect neuronal synchronization provides theoretical grounding for TMS therapy design:
Magnetic field effects on chimera states suggest new neuromodulation strategies:
The chimera framework provides a natural model for:
chimera state, magnetic field, hindmarsh-rose, neuronal network, traveling chimera, multicluster chimera, chimera breather, synchronization, coherence, incoherence, brain cells, transcranial magnetic stimulation, neuromodulation, collective dynamics