Rutger Hermsen (195605) · Figshare · 2022
<p>To help understand the conditions for the formation of colonies, a linear stability analysis studies whether, in an initially homogeneous population, small periodic density perturbations tend to grow. (See section <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1010612#sec012" target="_blank">Materials and methods</a> for the full derivations.) If they do, this leads to the formation of “colonies”. (A) For given model parameters, each wavelength is associated with an eigenvalue; if the eigenvalue is positive, density waves with this wavelength tend to grow. The figure plots the eigenvalue for a range of wavelengths as calculated for the default parameters of the 1D model (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1010612#pcbi.1010612.t001" target="_blank">Table 1</a>), additionally assuming all individuals have <i>ϕ</i> = 0.05. Perturbations with small wavelength are quenched by motility; those with a long wavelength by resource competition. In between, a window exists (gray shading) of wavelengths that have a positive eigenvalue. This explains the colony formation in the default parameters. The wavelength with the largest eigenvalue (indicated with the red dot and black arrow) provides a prediction for the wavelength—the distance between neighboring colonies. (B) The largest eigenvalue is plotted as a function of the spatial scales in the system: the scale of motility <i>σ</i><sub>m</sub> and the scale of competition <i>σ</i><sub>rc</sub>. (Remember that the scale of altruism <i>σ</i><sub>a</sub> is 1 by definition of the unit of length.) Otherwise, the assumptions are as in panel A. Colony formation is expected only in the linearly unstable regime, to the right of the red contour line. (C) For the same conditions used in panel B, the predicted wavelength is plotted. As a rule of thumb, it is somewhat smaller than 2<i>σ</i><sub>rc</sub>. (D) Simulations were performed for the parameters indicated with black symbols in panels B, C, E, and F, assuming that all individuals have an immutable level of altruism <i>ϕ</i> = 0.05. Shown are the resulting radial distribution functions. As expected, the system is nearly homogeneous at <i>σ</i><sub>rc</sub> = 1.5 (black circle, in the linearly stable regime), weak pair correlations are seen for <i>σ</i><sub>rc</sub> = 3.0 (marginally unstable), and strong correlations emerge for <i>σ</i><sub>rc</sub> = 4.5 (far in the unstable regime), indicating colony formation. (E) Simulation were performed for a large number of combinations of the spatial scales (19 × 21 = 399 in total); here, the variance of the local population density is plotted as a simple proxy for colony formation. Clearly, colonies form only in the parameter regime predicted in panel B. (F) For the simulations of panel E, the wavelength of the resulting colonies is plotted. (See section <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1010612#sec012" target="_blank">Materials and methods</a>.). The results agree broadly with the predictions of panel C.</p> <p>(TIFF)</p>
Cited by 0Open access
2018
This chapter illustrates the use of the Routh-Hurwitz test, and the application of the Nyquist stability criterion. Employing Routh-Hurwitz and Nyquist stability analyses, show that administration of inhaled 02 would eliminate Cheyne-Stokes breathing in the patient with congestive heart failure. The chapter employs a more intuitive approach by illustrating the basic notions underlying the Nyquist stability criterion. It considers the linear lung mechanics model with proportional feedback. As in the example of the lung mechanics model, the transient response and stability of the systems are determined by the poles of their closed-loop transfer functions. The relative stability of a given system can be quantified in terms of either the gain margin or the phase margin. The chapter also illustrates how the root locus method is applied. It concludes from Routh-Hurwitz analysis that the normal pupillary reflex is a highly stable negative feedback system.
Cited by 2
Jelen, Michal · Brno University of Technology Digital Library (Brno University of Technology) · 2012
Tato bakalářská práce se bude zabývat analýzou stability lineárních systémů. V teoretické části bude zmíněna stabilita a její podmínky, kritéria stability, jejich rozdělení do skupin a popis jednotlivých kritérií. V praktické části se vybere jedno kritérium stability se kterým se následně bude pracovat. Zkoumaným obvodem bude filtr s proudovými konvejory, jakožto aktivními prvky, ze kterého bude získán charakteristický polynom. V příkladech se bude pracovat s přenosovými funkcemi aktivních prvků prvního i druhého řádu. Bude vytvořen program, který umožní automatizovat Routhovo kritérium stability a vykreslení grafických výstupů v závislosti na vstupních parametrech a jejich hodnotách.
Cited by 0
Oleg N. Kirillov · 2021
Cited by 0
S. Palani · 2026
Cited by 0
Hildur Knútsdóttir A, Eirikur Pálsson B, Leah Edelstein-keshet A et al. · 2014
We model paracrine and autocrine signalling between breast tumor cells and macrophages. Analytical results are confirmed with discrete and continuum model simulations. Motility of breast tumor cells can be eliminated by changing certain model parameters. We identify parameters responsible for the observed tumor cell to macrophage ratio. Sensitivity of tumor cells to autocrine signalling affects their ability to migrate. a r t i c l e i n f o Article history:
Cited by 0
Chong Hoon Kwak, El-hang Lee · 2016
Cited by 0
Princeton University Press eBooks · 2013
Cited by 0
Angelo Luongo, Manuel Ferretti, Simona Di Nino · 2023
Cited by 0
Tesař, Lukáš · Brno University of Technology Digital Library (Brno University of Technology) · 2015
Tato práce pojednává o vyšetřování asymptotické stability lineárních diferenčních rovnic na základě kritéria Schurova-Cohnova a Routhova-Schurova. Obě tato kritéria jsou realizována v programu Maple a jejich použití je demonstrováno na příkladech. Na Adamsově-Bashforthově metodě pro řešení počátečních problémů obyčejných diferenciálních rovnic 1.řádu je ilustrováno použití techniky pro lokalizaci hranice oblasti asymptotické stability této metody.
Cited by 0Open access
H. Zohm · 2014
This chapter describes the equations governing linear stability of a magnetohydrodynamic (MHD) system. It presents the energy principle, which is a variational formalism for determining MHD stability. The principle is based on Ritz' variational principle for self-adjoint systems that was originally developed for fluid mechanics and has also been applied for example in quantum mechanics to estimate Eigenvalues for systems that are no longer analytically tractable. For the analysis of MHD stability of the tokamak using the energy functional, it is necessary to express δW in the appropriate co-ordinates. For the general axisymmetric case, this is done using the flux functions.
Cited by 0
Stefan Hein · elib (German Aerospace Center) · 2026
Cited by 0
Joe H. Chow, J.J. Sanchez-Gasca · 2019
This chapter presents the small-signal stability of power systems operating in “steady state,” that is, the system stability of an equilibrium point. The ability of the power system to track the load changes requires the power system to be small-signal stable, that is, a power system can stably move from one operating condition to a slightly different operating condition. The chapter discusses electromechanical modes in power systems and techniques to compute and identify the frequency and damping of these modes. The approach used is to develop linearized system models that are valid in a region about the equilibrium operating point. Electromechanical modes in a practical power system can be divided into three types: intraplant modes; local modes; and interarea modes. The chapter provides an overview of the development of linear models for nonlinear systems. There are two methods commonly used for generating linearized models: using analytical expressions, and using a numerical perturbation method.
Cited by 3
Haiyan Hu, Zaihua Wang · 2002
Cited by 1
Karan, Mehmet · Bilkent University Institutional Repository (Bilkent University) · 2016
Ankara :The Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent Univ. , 1990.
Cited by 0Open access
Khoo, Edwin · Zenodo (CERN European Organization for Nuclear Research) · 2023
Code and datasets for the Linear Stability Analysis of Transient Electrodeposition in Charged Porous Media: Suppression of Dendritic Growth by Surface Conduction paper
Cited by 0Open access
Thorwald Herbert · ICASE/NASA LaRC series · 1990
Cited by 7
Dong Xue-ping · 2004
In this paper, based on the analysis of the common Lyapunov function method and the multiple Lyapunov functions method which are used for the stability analysis of the linear switched system,a new method for the stability analysis is presented. The linear switched system is stable on the premise of all the stable subsystems when the time of each subsystem switched in is longer than its minmum dwell time. An example is given to demonstrate the application of the new method.
Cited by 0
Yves Aurégan, Claude Dépollier · Journal of Sound and Vibration · 1995
Cited by 58
Marco Aqil (10048398), Selen Atasoy (10048401), Morten L. Kringelbach (7184930) et al. · Figshare · 2021
<p>In order to compute meaningful spatiotemporal observables with CHAOSS for a given set of parameters, it is first necessary to find a steady state and compute its stability to perturbations. Here, we provide solutions to the steady-state equations and a general linear stability analysis for the Wilson-Cowan model on graphs.</p> <p>(PDF)</p>
Cited by 0Open access