The intricate architecture of dendritic arborization is fundamental to the formation and functionality of neural networks, serving as the primary site for synaptic integration and signal propagation. This study presents a pioneering computational model that simulates dendritic growth dynamics, employing exponential and logarithmic scaling over an extended developmental period of 720 days. This model offers a valuable tool for investigating the implications of diverse dendritic growth patterns on neural development, synaptic connectivity, and ultimately, cognitive functions. The computational framework incorporates biologically plausible parameters, allowing for the systematic exploration of dendritic branching patterns and their potential impact on neuronal information processing. By simulating exponential and logarithmic growth scales, the model captures the inherent complexity and diversity of dendritic morphologies observed in various neuronal populations across different brain regions. The findings from this study hold significant implications for our understanding of neural circuit assembly, synaptic integration, and the potential functional consequences of aberrant dendritic growth patterns observed in neurodevelopmental disorders. Furthermore, the model's ability to simulate extended developmental trajectories over a prolonged period of 720 days offers insights into the dynamic interplay between dendritic growth and synaptic pruning, which is crucial for the refinement and optimization of neural networks.

This article encapsulates an exploration of seizure dynamics through the lens of computational modeling in epilepsy. Starting with a foundational understanding of the FitzHugh-Nagumo model, asimplified representation of neuronal activity, we try to understand the intricacies of epileptic seizures. We methodically demonstrated the transition from normal neuronal activity to a seizure-like state by altering key parameters in the model, such as external current and coupling strength. This was followed by an extension of the model to a network of neurons, simulating the complex interactions and synchronization patterns indicative of seizure propagation. Numerical simulations were conducted to visualize the impact of varying coupling strengths on network dynamics, offering insights into the mechanisms of seizure initiation and spread. The study was complemented by a discussion on the implications of these findings for understanding epilepsy, highlighting the bridging of theoretical models with clinical understanding. Our approach not only illuminates the potential of computational models in epilepsy research but also underscores the significance of interdisciplinary collaboration in advancing our comprehension of neurological disorders. Through this article, we aim to provide a nuanced perspective on the modeling of epileptic seizures, offering a valuable resource for researchers and clinicians in the field.

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