Understanding the distribution of electrical potential within neurons is critical for advancing our comprehension of neuronal signaling and communication. Neurons, the fundamental units of the nervous system, rely on complex electrochemical processes to transmit information. The intricate structure of neurons, especially those with multiple dendrites, plays a crucial role in how these electrical signals are generated, propagated, and integrated. Despite significant progress in neuroscience, accurately modeling the electrical potential within neurons with elaborate dendritic architectures remains a challenge. This article introduces a novel approach to modeling the electrical potential in multi-dendritic neurons using Bessel functions, which offers a more precise and detailed representation of these processes. The proposed method involves solving the electric potential diffusion equation in cylindrical coordinates, a mathematical framework that naturally aligns with the geometry of dendrites. The radial and axial components of the solution are expressed using Bessel functions and sinusoidal functions, respectively. Bessel functions are particularly well-suited for this purpose due to their ability to describe waveforms in cylindrical systems, making them ideal for capturing the spatial variations in electrical potential within the cylindrical shape of dendrites. By leveraging this mathematical approach, we obtain a complete representation of the potential distribution across the neuron, from the soma (cell body) through the dendrites to the synaptic terminals. This model accurately captures the spatial variations of electrical potential in different regions of the neuron, including areas with complex dendritic arborizations, which are branching structures that significantly influence the neuron’s electrical characteristics. Simulation results underscore the effectiveness of this approach in reproducing realistic neuronal behavior. The model successfully mimics the way electrical signals propagate and interact within dendritic structures, providing crucial insights into the underlying mechanisms of signal integration and transmission in neurons.

Understanding the intricate and dynamic nature of brain disorders, such as epilepsy, Parkinson’s disease, and schizophrenia, presents a formidable challenge due to their inherent chaotic properties, which defy conventional analytical approaches. In response to this challenge, our research introduces a groundbreaking methodology aimed at simulating the chaotic behavior characteristic of these neurological conditions using advanced electrical circuit models. By conceptualizing the interactions among neurons and synapses as electrical components within our model, we endeavor to unravel the complex underlying mechanisms driving these disorders. Leveraging insights from chaos theory and drawing upon the rich toolkit of electrical engineering, our simulation framework offers a novel perspective on the ways in which disruptions within neural circuits manifest as pathological states, shedding light on the intricate dynamics of brain diseases. Through rigorous numerical simulations and thorough analysis, we illustrate the efficacy of our approach in deciphering the chaotic dynamics inherent in these disorders, thus laying the foundation for the development of innovative therapeutic interventions. Furthermore, our research underscores the paramount importance of fostering interdisciplinary collaboration between the fields of neuroscience and electrical engineering; as such, synergistic partnerships hold the key to unlocking new frontiers in understanding and effectively treating complex neurological disorders, thus paving the way for improved patient outcomes and enhanced quality of life.

This paper investigates the simulation of brain chaos dynamics using a combination of the Chua circuit and diode tunnel mechanisms, aiming to examine chaotic behavior in brain networks. Leveraging the inherent chaotic properties of the Chua circuit, Fitzhugh-Nagumo (FHN) function and the nonlinear characteristics of diode tunneling, our model offers a platform to mimic the intricate synaptic interactions observed in the brain. By subjecting the model to various stimuli and perturbations, we analyze the emergence and evolution of chaotic patterns, shedding light on the underlying mechanisms of cerebral chaos. Through numerical simulations and experimental validation, we demonstrate the effectiveness of our approach in replicating key features of brain chaos and highlight its potential implications for understanding neurological disorders and cognitive processes. This research contributes to the broader effort of leveraging computational models to explore the complex dynamics of the brain and their implications for neuroscience and microengineering.