Related papers: Mathematical Models of Bipolar Disorder
Infectious diseases often involve multiple strains that interact through the immune response generated after an infection. This study investigates the conditions under which a two-strain epidemic model with partial cross-immunity can lead…
Individuals with bipolar disorder tend to cycle through disease states such as depression and mania. The heterogeneous nature of disease across states complicates the evaluation of interventions for bipolar disorder patients, as varied…
Bipolar disorder (BPD) is a chronic mental illness characterized by extreme mood and energy changes from mania to depression. These changes drive behaviors that often lead to devastating personal or social consequences. BPD is managed…
We propose a method for estimating the asymptotic phase and amplitude functions of limit-cycle oscillators using observed time series data without prior knowledge of their dynamical equations. The estimation is performed by polynomial…
In this work we study the Brusselator - a prototypical model for chemical oscillations - under the assumption that the bifurcation parameter is of order $O(1/\epsilon)$ for positive $\epsilon\ll 1$. The dynamics of this mathematical model…
Synchronization and desynchronization are the two ends on the spectrum of emergent phenomena that somehow often coexist in biological, neuronal, and physical networks. However, previous studies essentially regard their coexistence as a…
Diagnosing cognitive (mental health) disorders is a delicate and complex task. Identifying the next most informative symptoms to assess, in order to distinguish between possible disorders, presents an additional challenge. This process…
A theoretical framework is developed for a precise control of spatial patterns in oscillatory media using nonlinear global feedback, where a proper form of the feedback function corresponding to a specific pattern is predicted through the…
Purpose of review: We review the literature on the use and potential use of computational psychiatry methods in Borderline Personality Disorder. Recent findings: Computational approaches have been used in psychiatry to increase our…
Different dependence scenarios can arise in multivariate extremes, entailing careful selection of an appropriate class of models. In bivariate extremes, the variables are either asymptotically dependent or are asymptotically independent.…
The one-dimensional harmonic oscillator in a box problem is possibly the simplest example of a two-mode system. This system has two exactly solvable limits, the harmonic oscillator and a particle in a (one-dimensional) box. Each of the two…
A biochemical oscillator model, describing developmental stage of myxobacteria, is analyzed mathematically. Observations from numerical simulations show that in a certain range of parameters, the corresponding system of ordinary…
We extend the well-known method of calculating bulk correlation functions of the conformal Ising model via bosonisation to situations with boundaries. Oshikawa and Affleck have found the boundary states of two decoupled Ising models in…
The effects of noise on the dynamics of nonlinear systems is known to lead to many counter-intuitive behaviors. Using simple planar limit cycle oscillators, we show that the addition of moderate noise leads to qualitatively different…
We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electrooptic modulation…
Seven out of ten people with bipolar disorder are initially misdiagnosed and thirty percent of individuals with bipolar disorder will commit suicide. Identifying the early phases of the disorder is one of the key components for reducing the…
Multiple Sclerosis is a degenerative condition of the central nervous system that affects nearly 2.5 million of individuals in terms of their physical, cognitive, psychological and social capabilities. Researchers are currently…
Control systems are usually modeled by differential equations describing how physical phenomena can be influenced by certain control parameters or inputs. Although these models are very powerful when dealing with physical phenomena, they…
Oscillator models are central to the study of system properties such as entrainment or synchronization. Due to their nonlinear nature, few system-theoretic tools exist to analyze those models. The paper develops a sensitivity analysis for…
Bipolar disorder (BD) and borderline personality disorder (BPD) are two chronic mental health conditions that clinicians find challenging to distinguish based on clinical interviews, due to their overlapping symptoms. In this work, we…