Brain oscillations are a measurable characteristic of collective neuronal activity and reflect the dynamic organisation of the nervous system across multiple timescales. The main bands of the electroencephalogram (EEG), i.e., Delta (0.5–4 Hz), Theta (4–7 Hz), Alpha (8–12 Hz), Beta (13–30 Hz) and Gamma (30–100 Hz), are conventionally associated with functional and cognitive states, although their interpretation in terms of general dynamic principles remains an open question. This paper proposes a minimal physical-mathematical model for investigating selected spectral properties associated with neural oscillations. The model consists of a linear chain of identical elastically coupled masses. The normal modes of the system are obtained by solving the associated eigenvalue problem, using a global-local optimization process to align the model eigenfrequencies with representative frequencies of the five EEG bands. More specifically, the Basin-hopping and Powell algorithms are combined to explore the parameter space and minimise deviations from the prescribed target frequencies. The results achieved show quantitative alignment within numerical tolerance between simulated frequencies and target reference frequencies. This agreement is interpreted as the solution of an inverse spectral fitting problem rather than as independent validation of a mechanism generating neural oscillations. A 50-run multi-start analysis showed high spectral reproducibility despite substantial variability in the optimized parameters, while local sensitivity analysis revealed a structured, mode-dependent response to parameter perturbations. The parallelism between physical and biological systems does not lie in a direct correspondence between components, and the model is not intended to reproduce specific neuronal or synaptic mechanisms. The results thus indicate that a highly simplified coupled system can provide a mathematically transparent framework for investigating relationships between coupling parameters, eigenfrequencies and collective modes, opening up prospects for future applications in neural system modelling.
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Neural Oscillations Model Using Basin-Hopping Optimization
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Received: 02 Feb 2026 | Revised: 21 Aug 2026 | Accepted: 14 Sep 2026 | Published: 12 Oct 2026
Abstract
References
- 1.
Niedermeyer, E.; Lopes da Silva, F.H. (Eds.) Electroencephalography: Basic Principles, Clinical Applications, and Related Fields, 5th ed.; Lippincott Williams & Wilkins: Philadelphia, PA, USA, 2005.
- 2.
Buzsáki, G. Rhythms of the Brain; Oxford University Press: Oxford, UK, 2006. https://doi.org/10.1093/acprof:oso/9780195301069.001.0001.
- 3.
Buzsáki, G.; Draguhn, A. Neuronal oscillations in cortical networks. Science 2004, 304, 1926–1929. https://doi.org/10.1126/science.1099745.
- 4.
Fries, P. Rhythms for Cognition: Communication through Coherence. Neuron 2015, 88, 220–235. https://doi.org/10.1016/j.neuron.2015.09.034.
- 5.
Başar, E.; Başar-Eroglu, C.; Karakaş, S.; et al. Gamma, alpha, delta, and theta oscillations govern cognitive processes. Int. J. Psychophysiol. 2001, 39, 241–248. https://doi.org/10.1016/S0167-8760(00)00145-8.
- 6.
Wang, X.J. Neurophysiological and Computational Principles of Cortical Rhythms in Cognition. Physiol. Rev. 2010, 90, 1195–1268. https://doi.org/10.1152/physrev.00035.2008.
- 7.
Strogatz, S.H. Exploring complex networks. Nature 2001, 410, 268–276. https://doi.org/10.1038/35065725.
- 8.
Breakspear, M.; Heitmann, S.; Daffertshofer, A. Generative Models of Cortical Oscillations: Neurobiological Implications of the Kuramoto Model. Front. Hum. Neurosci. 2010, 4, 190. https://doi.org/10.3389/fnhum.2010.00190.
- 9.
Uhlhaas, P.J.; Roux, F.; Rodriguez, E.; et al. Neural synchrony and the development of cortical networks. Trends Cogn. Sci. 2010, 14, 72–80. https://doi.org/10.1016/j.tics.2009.12.002.
- 10.
Magazù, S.; Caccamo, M.T. Parametric resonance brain model. Sci. Rep. 2024, 14, 24657. https://doi.org/10.1038/s41598-024-76610-8.
- 11.
Madadi Asl, M.; Valizadeh, A. Entrainment by transcranial alternating current stimulation: Insights from models of cortical oscillations and dynamical systems theory. Phys. Life Rev. 2025, 53, 147–176. https://doi.org/10.1016/j.plrev.2025.03.008.
- 12.
Pikovsky, A.; Rosenblum, M.; Kurths, J. Synchronization: A Universal Concept in Nonlinear Sciences; Cambridge University Press: Cambridge, UK, 2001. https://doi.org/10.1017/CBO9780511755743.
- 13.
Arenas, A.; Díaz-Guilera, A.; Kurths, J.; et al. Synchronization in complex networks. Phys. Rep. 2008, 469, 93–153. https://doi.org/10.1016/j.physrep.2008.09.002.
- 14.
Atasoy, S.; Donnelly, I.; Pearson, J. Human brain networks function in connectome-specific harmonic waves. Nat. Commun. 2016, 7, 10340. https://doi.org/10.1038/ncomms10340.
- 15.
Musotto, R.; Wanderlingh, U.; Pioggia, G. Ca2+ waves in astrocytes: Computational modeling and experimental data. Front. Cell. Neurosci. 2025, 19, 1536096. https://doi.org/10.3389/fncel.2025.1536096.
- 16.
Musotto, R.; Wanderlingh, U.; D’Ascola, A.; et al. Dynamics of astrocytes Ca2+ signaling: A low-cost fluorescence customized system for 2D cultures. Front. Cell Dev. Biol. 2024, 12, 1320672. https://doi.org/10.3389/fcell.2024.1320672.
- 17.
Hodgkin, A.L.; Huxley, A.F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 1952, 117, 500–544. https://doi.org/10.1113/jphysiol.1952.sp004764.
- 18.
Breakspear, M. Dynamic models of large-scale brain activity. Nat. Neurosci. 2017, 20, 340–352. https://doi.org/10.1038/nn.4497.
- 19.
Musotto, R.; Pioggia, G. Neuromechanical network model. Front. Phys. 2025, 13, 1656677. https://doi.org/10.3389/fphy.2025.1656677.
- 20.
Wales, D.J.; Doye, J.P.K. Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms. J. Phys. Chem. A 1997, 101, 5111–5116. https://doi.org/10.1021/jp970984n.
- 21.
Röder, K.; Wales, D.J. Mutational Basin-Hopping: Combined Structure and Sequence Optimization for Biomolecules. J. Phys. Chem. Lett. 2018, 9, 6169–6173. https://doi.org/10.1021/acs.jpclett.8b02839.
- 22.
Powell, M.J.D. An efficient method for finding the minimum of a function of several variables without calculating derivatives. Comput. J. 1964, 7, 155–162. https://doi.org/10.1093/comjnl/7.2.155.
- 23.
Doelling, K.B.; Assaneo, M.F. Neural oscillations are a start toward understanding brain activity rather than the end. PLoS Biol. 2021, 19, e3001234. https://doi.org/10.1371/journal.pbio.3001234.
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