6,445 research outputs found
On the boundedness of some nonlinear differential equation of second order
In this paper we study the boundedness of the solutions of some nonlinear dofferential equation using as a key tool the Second Lyapunov method, i.e. find sufficient conditions under which the solutions of this equation are bounded. Variuos particular cases and methodological remarks are included at the end of paper.Fil: Guzmán, Paulo Matias. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Napoles Valdes, Juan Eduardo. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; ArgentinaFil: Lugo, Luciano Miguel. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; Argentin
The determination of asymptotic and periodic behavior of dynamic systems arising in control system analysis Final report
Asymptotic and periodic behavior prediction for nonlinear control system with mathematical model of rigid body vehicl
Space-time resonances
This article is a short exposition of the space-time resonances method. It
was introduced by Masmoudi, Shatah, and the author, in order to understand
global existence for nonlinear dispersive equations, set in the whole space,
and with small data. The idea is to combine the classical concept of
resonances, with the feature of dispersive equations: wave packets propagate at
a group velocity which depends on their frequency localization. The analytical
method which follows from this idea turns out to be a very general tool.Comment: 10 page
Hopf bifurcation in a gene regulatory network model: Molecular movement causes oscillations
Gene regulatory networks, i.e. DNA segments in a cell which interact with each other indirectly through their RNA and protein products, lie at the heart of many important intracellular signal transduction processes. In this paper we analyse a mathematical model of a canonical gene regulatory network consisting of a single negative feedback loop between a protein and its mRNA (e.g. the Hes1 transcription factor system). The model consists of two partial differential equations describing the spatio-temporal interactions between the protein and its mRNA in a 1-dimensional domain. Such intracellular negative feedback systems are known to exhibit oscillatory behaviour and this is the case for our model, shown initially via computational simulations. In order to investigate this behaviour more deeply, we next solve our system using Greens functions and then undertake a linearized stability analysis of the steady states of the model. Our results show that the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. This shows that the spatial movement of the mRNA and protein molecules alone is sufficient to cause the oscillations. This has implications for transcription factors such as p53, NF-B and heat shock proteins which are involved in regulating important cellular processes such as inflammation, meiosis, apoptosis and the heat shock response, and are linked to diseases such as arthritis and cancer
Amplitude bounds for biochemical oscillators
We present a practical method to obtain bounds for the oscillation minima and
maxima of large classes of biochemical oscillator models that generate
oscillations through a negative feedback. These bounds depend on the feedback
nonlinearity and are independent of explicit or effective feedback delays. For
specific systems, we obtain explicit analytical expressions for the bounds and
demonstrate their effectiveness in comparison with numerical simulations.Comment: 6 pages, 4 figure
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