Global dynamics of a delay differential system of a two-patch SIS-model with transport-related infections

Yukihiko Nakata; Gergely Röst

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Displaying similar documents to “Global dynamics of a delay differential system of a two-patch SIS-model with transport-related infections”

The Dynamics of an Interactional Model of Rabies Transmitted between Human and Dogs

Wei Yang, Jie Lou (2009)

Bollettino dell'Unione Matematica Italiana

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Assuming that the population of dogs is constant and the population of human satisfies the Logistical model, an interactional model of rabies transmitted between human and dogs is formulated. Two thresholds $R_{0}$ and $R_{1}$ which determine the outcome of the disease are identified. Utilizing the method of Lyapunov function and the property of the cooperative systems, we get the global asymptotic stability for both the disease-free equilibrium and the endemic equilibrium. A critical vaccination...

Chaotic behaviour of continuous dynamical system generated by Euler equation branching and its application in macroeconomic equilibrium model

Barbora Volná (2015)

Mathematica Bohemica

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We focus on the special type of the continuous dynamical system which is generated by Euler equation branching. Euler equation branching is a type of differential inclusion $\dot{x} \in {f (x), g (x)}$ , where $f, g : X \subset ℝ^{n} \to ℝ^{n}$ are continuous and $f (x) \neq g (x)$ at every point $x \in X$ . It seems this chaotic behaviour is typical for such dynamical system. In the second part we show an application in a new formulated overall macroeconomic equilibrium model. This new model is based on the fundamental macroeconomic aggregate equilibrium model called...

Steady state in a biological system: global asymptotic stability

Maria Adelaide Sneider (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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A suitable Liapunov function is constructed for proving that the unique critical point of a non-linear system of ordinary differential equations, considered in a well determined polyhedron $K$ , is globally asymptotically stable in $K$ . The analytic problem arises from an investigation concerning a steady state in a particular macromolecular system: the visual system represented by the pigment rhodopsin in the presence of light.

Steady state in a biological system: global asymptotic stability

Maria Adelaide Sneider (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Stable solutions of $- Δ u = f (u)$ in $ℝ^{N}$

Louis Dupaigne, Alberto Farina (2010)

Journal of the European Mathematical Society

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Several Liouville-type theorems are presented for stable solutions of the equation $- Δ u = f (u)$ in $ℝ^{N}$ , where $f > 0$ is a general convex, nondecreasing function. Extensions to solutions which are merely stable outside a compact set are discussed.

Stabilization of monomial maps in higher codimension

Jan-Li Lin, Elizabeth Wulcan (2014)

Annales de l’institut Fourier

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A monomial self-map $f$ on a complex toric variety is said to be $k$ -stable if the action induced on the $2 k$ -cohomology is compatible with iteration. We show that under suitable conditions on the eigenvalues of the matrix of exponents of $f$ , we can find a toric model with at worst quotient singularities where $f$ is $k$ -stable. If $f$ is replaced by an iterate one can find a $k$ -stable model as soon as the dynamical degrees $λ_{k}$ of $f$ satisfy $λ_{k}^{2} > λ_{k - 1} λ_{k + 1}$ . On the other hand, we give examples of monomial maps $f$ , where...

Delay-dependent stability conditions for fundamental characteristic functions

Hideaki Matsunaga (2023)

Archivum Mathematicum

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This paper is devoted to the investigation on the stability for two characteristic functions $f_{1} (z) = z^{2} + p e^{- z τ} + q$ and $f_{2} (z) = z^{2} + p z e^{- z τ} + q$ , where $p$ and $q$ are real numbers and $τ > 0$ . The obtained theorems describe the explicit stability dependence on the changing delay $τ$ . Our results are applied to some special cases of a linear differential system with delay in the diagonal terms and delay-dependent stability conditions are obtained.

Solutions of an advance-delay differential equation and their asymptotic behaviour

Gabriela Vážanová (2023)

Archivum Mathematicum

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The paper considers a scalar differential equation of an advance-delay type $\dot{y} (t) = - (a_{0} + \frac{a_{1}}{t}) y (t - τ) + (b_{0} + \frac{b_{1}}{t}) y (t + σ),$ where constants $a_{0}$ , $b_{0}$ , $τ$ and $σ$ are positive, and $a_{1}$ and $b_{1}$ are arbitrary. The behavior of its solutions for $t \to \infty$ is analyzed provided that the transcendental equation $λ = - a_{0} e^{- λ τ} + b_{0} e^{λ σ}$ has a positive real root. An exponential-type function approximating the solution is searched for to be used in proving the existence of a semi-global solution. Moreover, the lower and upper estimates are given for such a solution.

Simultaneous stabilization in $A_{ℝ} ()$

Raymond Mortini, Brett D. Wick (2009)

Studia Mathematica

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We study the problem of simultaneous stabilization for the algebra $A_{ℝ} ()$ . Invertible pairs $(f_{j}, g_{j})$ , j = 1,..., n, in a commutative unital algebra are called simultaneously stabilizable if there exists a pair (α,β) of elements such that $α f_{j} + β g_{j}$ is invertible in this algebra for j = 1,..., n. For n = 2, the simultaneous stabilization problem admits a positive solution for any data if and only if the Bass stable rank of the algebra is one. Since $A_{ℝ} ()$ has stable rank two, we are faced here with a different...

A new look at an old comparison theorem

Jaroslav Jaroš (2021)

Archivum Mathematicum

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We present an integral comparison theorem which guarantees the global existence of a solution of the generalized Riccati equation on the given interval $[a, b)$ when it is known that certain majorant Riccati equation has a global solution on $[a, b)$ .