Version 1
: Received: 29 June 2024 / Approved: 1 July 2024 / Online: 1 July 2024 (13:13:32 CEST)
How to cite:
Montgomery, R. Insights into Psychiatric Diseases Represented by Wave Equations: A Mathematical and Graphical Exploration. Preprints2024, 2024070090. https://doi.org/10.20944/preprints202407.0090.v1
Montgomery, R. Insights into Psychiatric Diseases Represented by Wave Equations: A Mathematical and Graphical Exploration. Preprints 2024, 2024070090. https://doi.org/10.20944/preprints202407.0090.v1
Montgomery, R. Insights into Psychiatric Diseases Represented by Wave Equations: A Mathematical and Graphical Exploration. Preprints2024, 2024070090. https://doi.org/10.20944/preprints202407.0090.v1
APA Style
Montgomery, R. (2024). Insights into Psychiatric Diseases Represented by Wave Equations: A Mathematical and Graphical Exploration. Preprints. https://doi.org/10.20944/preprints202407.0090.v1
Chicago/Turabian Style
Montgomery, R. 2024 "Insights into Psychiatric Diseases Represented by Wave Equations: A Mathematical and Graphical Exploration" Preprints. https://doi.org/10.20944/preprints202407.0090.v1
Abstract
Psychiatric disorders, characterized by complex and fluctuating patterns of thoughts, emotions, and behaviors, can be effectively modeled and visualized using mathematical wave equations. This study explores the representation of three major psychiatric conditions— Psychosis, Bipolar Disorder and Obsessive Compulsive Disorder (OCD)—through the application of differential equations, damping factors, and noise perturbations. Psychosis is modeled using Lissajous figures with high-frequency components, damping, and noise, symbolizing the irregular and erratic thought patterns characteristic of this condition. The inclusion of random perturbations and varying frequencies illustrates the chaotic and unpredictable nature of psychotic episodes, while damping effects reflect the temporary reductions in symptom intensity. For bipolar disorder, a system of partial differential equations simulates the cyclical nature of manic and depressive episodes. The model captures high-energy manic phases with periodic disturbances and the subsequent transition to lower-energy depressive states through damping effects. This representation highlights the oscillatory behavior and recurring episodes inherent to bipolar disorder. OCD is represented with Circumferential Complex Equations in Mult directions. The resulting graphical representations provide intuitive visual insights into the dynamics of these psychiatric disorders. By leveraging wave equations and mathematical modeling, this approach offers a novel perspective on understanding and analyzing the complex behaviors associated with OCD, bipolar disorder and psychosis. This method not only aids in the conceptualization of psychiatric phenomena but also underscores the potential of mathematical tools in the study of mental health conditions.
Keywords
Keywords: Psychosis, Bipolar Disorder and Obsessive Compulsive Disorder, Simulation with waves and differential equations
Subject
Biology and Life Sciences, Neuroscience and Neurology
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
