preprints.org > computer science and mathematics > mathematical and computational biology > doi: 10.20944/preprints202404.1389.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 21 April 2024 / Approved: 22 April 2024 / Online: 22 April 2024 (10:28:53 CEST)

The complex dynamics of the neocortex, the outermost layer of the brain, have been a subject of intense research in neuroscience. Recent studies have suggested that magnetic fields generated by neuronal activity may play a significant role in neocortical dynamics. This paper presents a simplified mathematical model that explores the hypothesized interactions between magnetic dynamos, nondissipative systems, Hamiltonian equations, and the Lorenz force in the context of neocortical dynamics. The proposed model is based on a set of coupled Hamiltonian equations inspired by the Lorenz system, a well-known chaotic dynamical system. The generalized coordinates in the model represent the magnetic field components, while the generalized momenta are related to the electric field components or other relevant quantities. The Hamiltonian equations describe the conservative dynamics of the system, and the coupling terms in the equations are interpreted as representing the interactions between the magnetic and electric field components, analogous to the Lorenz force in electromagnetism. The model is implemented using Python, and the Hamiltonian equations are numerically solved using the odeint function from the scipy.integrate module. The resulting dynamics of the magnetic field components are visualized using matplotlib. While the model is highly simplified and does not capture the full complexity of neocortical dynamics, it serves as a starting point for investigating the potential role of magnetic dynamos and Lorenz force interactions in the brain. The paper discusses the limitations of the current model and highlights the need for further refinements, such as incorporating more realistic biological constraints, considering energy dissipation and compensation mechanisms, and validating the model against experimental data. Future work should focus on developing a more comprehensive and biologically plausible model that integrates the latest findings from neuroscience, physics, and computational modeling. By presenting this simplified Hamiltonian model, the paper aims to stimulate further research and discussion on the potential significance of magnetic dynamos and Lorenz force interactions in neocortical dynamics. The model provides a framework for exploring these hypothesized mechanisms and may guide future experimental and theoretical investigations in this emerging field of neuroscience

Hamiltonian Model; Magnetic Dynamos; Lorenz Force Interactions; Neocortical Dynamics

Computer Science and Mathematics, Mathematical and Computational Biology

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