Related papers: Mathematical Models of Bipolar Disorder
The behaviour of a space-modulated, so-called "argumental" oscillator is studied, which is represented by a model having an even-parity space-modulating function. Analytic expressions of a stability criterion and of discrete energy levels…
We consider the one-dimensional Glauber dynamics with coupling disorder in terms of bilinear fermion Hamiltonians. Dynamic exponents embodied in the spectrum gap of these latter are evaluated numerically by averaging over both binary and…
We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear…
Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyze the future asymptotics of models which exhibit oscillatory behavior, we provide a theorem concerning the large-time…
Depression is a complex mental disorder characterized by a diverse range of observable and measurable indicators that go beyond traditional subjective assessments. Recent research has increasingly focused on objective, passive, and…
In this work, a mathematical model of self-oscillatory dynamics of the metabolism in a cell is studied. The full phase-parametric characteristics of variations of the form of attractors depending on the dissipation of a kinetic membrane…
The illness-death model for chronic conditions is combined with a renewal equation for the number of newborns taking into account possibly different fertility rates in the healthy and diseased parts of the population. The resulting boundary…
The double empathy problem recasts the difficulty of forming empathy bonds in social interactions between autistic and neurotypical individuals as a bidirectional problem, rather than due to a deficit exclusive to the person on the…
Recurrent major mood episodes and subsyndromal mood instability cause substantial disability in patients with bipolar disorder. Early identification of mood episodes enabling timely mood stabilisation is an important clinical goal. Recent…
We study the dynamics of a dilute spherical model with two body interactions and random exchanges. We analyze the Langevin equations and we introduce a functional variational method to study generic dilute disordered models. A crossover…
Due to existence of periodic windows, chaotic systems undergo numerous bifurcations as system parameters vary, rendering it hard to employ an analytic continuation, which constitutes a major obstacle for its effective analysis or…
We propose a quite general model of active media by consideration of the interaction between pacemakers via their phase response curves. This model describes a network of pulse oscillators coupled by their response to the internal…
We study the pattern dynamics in a reaction diffusion model of the activator--inhibitor type in the oscillatory regime. We consider finite systems with partially absorptive boundary conditions analizing examples in different geometries in…
Disordered biopolymer gels have striking mechanical properties including strong nonlinearities. In the case of athermal gels (such as collagen-I) the nonlinearity has long been associated with a crossover from a bending dominated to a…
In this paper we study the family of planar hybrid differential systems formed by two linear centers and a polynomial reset map of any degree. We study their limit cycles and also provide examples of these hybrid systems exhibiting chaotic…
Cycles of word usage have been described using an integro-differential Volterra model close to a Hopf bifurcation. Here we transform this system to a phase model, which allows us to phase-couple the words and address the observation of…
Complex dynamical systems may exhibit multiple steady states, including time-periodic limit cycles, where the final trajectory depends on initial conditions. With tuning of parameters, limit cycles can proliferate or merge at an exceptional…
We study two body dipolar scattering with one dimension of confinement. We include the effects of confinement by expanding this degree of freedom in harmonic oscillator states. We then study the properties of the resulting multi-channel…
A new method is presented for the analysis of limit cycle oscillations in mixed-feedback systems. The calculation of the limit cycle is reformulated as the zero finding of a mixed-monotone relation, that is, of the difference of two…
Symbolic models are abstract descriptions of continuous systems in which symbols represent aggregates of continuous states. In the last few years there has been a growing interest in the use of symbolic models as a tool for mitigating…