Displaying similar documents to “Steady state in a biological system: global asymptotic stability”

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

Similarity:

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.

Asymptotic properties of ground states of scalar field equations with a vanishing parameter

Vitaly Moroz, Cyrill B. Muratov (2014)

Journal of the European Mathematical Society

Similarity:

We study the leading order behaviour of positive solutions of the equation - Δ u + ϵ u - | u | p - 2 u + | u | q - 2 u = 0 , x N , where N 3 , q > p > 2 and when ϵ > 0 is a small parameter. We give a complete characterization of all possible asymptotic regimes as a function of p , q and N . The behavior of solutions depends sensitively on whether p is less, equal or bigger than the critical Sobolev exponent 2 * = 2 N N - 2 . For p < 2 * the solution asymptotically coincides with the solution of the equation in which the last term is absent. For p > 2 * the solution asymptotically...

Asymptotic behavior of a sequence defined by iteration with applications

Stevo Stević (2002)

Colloquium Mathematicae

Similarity:

We consider the asymptotic behavior of some classes of sequences defined by a recurrent formula. The main result is the following: Let f: (0,∞)² → (0,∞) be a continuous function such that (a) 0 < f(x,y) < px + (1-p)y for some p ∈ (0,1) and for all x,y ∈ (0,α), where α > 0; (b) f ( x , y ) = p x + ( 1 - p ) y - s = m s ( x , y ) uniformly in a neighborhood of the origin, where m > 1, s ( x , y ) = i = 0 s a i , s x s - i y i ; (c) ( 1 , 1 ) = i = 0 m a i , m > 0 . Let x₀,x₁ ∈ (0,α) and x n + 1 = f ( x , x n - 1 ) , n ∈ ℕ. Then the sequence (xₙ) satisfies the following asymptotic formula: x ( ( 2 - p ) / ( ( m - 1 ) i = 0 m a i , m ) ) 1 / ( m - 1 ) 1 / n m - 1 .

Numerical stability of the intrinsic equations for beams in time domain

Klesa, Jan

Similarity:

Intrinsic equations represent promising approach for the description of rotor blade dynamics. They are the system of non-linear partial differential equations. Stability of numeric solution by the finite difference method is described. The stability is studied for various numerical schemes with different methods for the computation of spatial derivatives from time level n + 0 . 5 (i.e., mean values of old and new time step) to n + 1 (i.e., only from new time step). Stable solution was obtained only...

Quantitative stability for sumsets in n

Alessio Figalli, David Jerison (2015)

Journal of the European Mathematical Society

Similarity:

Given a measurable set A n of positive measure, it is not difficult to show that | A + A | = | 2 A | if and only if A is equal to its convex hull minus a set of measure zero. We investigate the stability of this statement: If ( | A + A | - | 2 A | ) / | A | is small, is A close to its convex hull? Our main result is an explicit control, in arbitrary dimension, on the measure of the difference between A and its convex hull in terms of ( | A + A | - | 2 A | ) / | A | .

Lyapunov functions and L p -estimates for a class of reaction-diffusion systems

Dirk Horstmann (2001)

Colloquium Mathematicae

Similarity:

We give a sufficient condition for the existence of a Lyapunov function for the system aₜ = ∇(k(a,c)∇a - h(a,c)∇c), x ∈ Ω, t > 0, ε c = k c Δ c - f ( c ) c + g ( a , c ) , x ∈ Ω, t > 0, for Ω N , completed with either a = c = 0, or ∂a/∂n = ∂c/∂n = 0, or k(a,c) ∂a/∂n = h(a,c) ∂c/∂n, c = 0 on ∂Ω × t > 0. Furthermore we study the asymptotic behaviour of the solution and give some uniform L p -estimates.

Existence and asymptotic behavior of positive solutions for elliptic systems with nonstandard growth conditions

Honghui Yin, Zuodong Yang (2012)

Annales Polonici Mathematici

Similarity:

Our main purpose is to establish the existence of a positive solution of the system ⎧ - p ( x ) u = F ( x , u , v ) , x ∈ Ω, ⎨ - q ( x ) v = H ( x , u , v ) , x ∈ Ω, ⎩u = v = 0, x ∈ ∂Ω, where Ω N is a bounded domain with C² boundary, F ( x , u , v ) = λ p ( x ) [ g ( x ) a ( u ) + f ( v ) ] , H ( x , u , v ) = λ q ( x ) [ g ( x ) b ( v ) + h ( u ) ] , λ > 0 is a parameter, p(x),q(x) are functions which satisfy some conditions, and - p ( x ) u = - d i v ( | u | p ( x ) - 2 u ) is called the p(x)-Laplacian. We give existence results and consider the asymptotic behavior of solutions near the boundary. We do not assume any symmetry conditions on the system.

Asymptotic integration of differential equations with singular p -Laplacian

Milan Medveď, Eva Pekárková (2016)

Archivum Mathematicum

Similarity:

In this paper we deal with the problem of asymptotic integration of nonlinear differential equations with p - Laplacian, where 1 < p < 2 . We prove sufficient conditions under which all solutions of an equation from this class are converging to a linear function as t .

Asymptotic analysis and sign-changing bubble towers for Lane–Emden problems

Francesca De Marchis, Isabella Ianni, Filomena Pacella (2015)

Journal of the European Mathematical Society

Similarity:

We consider the semilinear Lane–Emden problem where p > 1 and Ω is a smooth bounded domain of 2 . The aim of the paper is to analyze the asymptotic behavior of sign changing solutions of ( p ) , as p + . Among other results we show, under some symmetry assumptions on Ω , that the positive and negative parts of a family of symmetric solutions concentrate at the same point, as p + , and the limit profile looks like a tower of two bubbles given by a superposition of a regular and a singular solution of...

Practical h -stability behavior of time-varying nonlinear systems

Abir Kicha, Hanen Damak, Mohamed Ali Hammami (2023)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We deal with the problem of practical uniform h -stability for nonlinear time-varying perturbed differential equations. The main aim is to give sufficient conditions on the linear and perturbed terms to guarantee the global existence and the practical uniform h -stability of the solutions based on Gronwall’s type integral inequalities. Several numerical examples and an application to control systems with simulations are presented to illustrate the applicability of the obtained results. ...

Global stability of travelling fronts for a damped wave equation with bistable nonlinearity

Thierry Gallay, Romain Joly (2009)

Annales scientifiques de l'École Normale Supérieure

Similarity:

We consider the damped wave equation α u t t + u t = u x x - V ' ( u ) on the whole real line, where V is a bistable potential. This equation has travelling front solutions of the form u ( x , t ) = h ( x - s t ) which describe a moving interface between two different steady states of the system, one of which being the global minimum of V . We show that, if the initial data are sufficiently close to the profile of a front for large | x | , the solution of the damped wave equation converges uniformly on to a travelling front as t + . The proof of this...

Exponential stability conditions for non-autonomous differential equations with unbounded commutators in a Banach space

Michael Gil&#039; (2023)

Czechoslovak Mathematical Journal

Similarity:

We consider the equation d y ( t ) / d t = ( A + B ( t ) ) y ( t ) ( t 0 ) , where A is the generator of an analytic semigroup ( e A t ) t 0 on a Banach space 𝒳 , B ( t ) is a variable bounded operator in 𝒳 . It is assumed that the commutator K ( t ) = A B ( t ) - B ( t ) A has the following property: there is a linear operator S having a bounded left-inverse operator S l - 1 such that S e A t is integrable and the operator K ( t ) S l - 1 is bounded. Under these conditions an exponential stability test is derived. As an example we consider a coupled system of parabolic equations. ...

Simultaneous stabilization in A ( )

Raymond Mortini, Brett D. Wick (2009)

Studia Mathematica

Similarity:

We study the problem of simultaneous stabilization for the algebra A ( ) . 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 ( ) has stable rank two, we are faced here with a different...

Recent results on stationary critical Kirchhoff systems in closed manifolds

Emmanuel Hebey, Pierre-Damien Thizy (2013-2014)

Séminaire Laurent Schwartz — EDP et applications

Similarity:

We report on results we recently obtained in Hebey and Thizy [11, 12] for critical stationary Kirchhoff systems in closed manifolds. Let ( M n , g ) be a closed n -manifold, n 3 . The critical Kirchhoff systems we consider are written as a + b j = 1 p M | u j | 2 d v g Δ g u i + j = 1 p A i j u j = U 2 - 2 u i for all i = 1 , , p , where Δ g is the Laplace-Beltrami operator, A is a C 1 -map from M into the space M s p ( ) of symmetric p × p matrices with real entries, the A i j ’s are the components of A , U = ( u 1 , , u p ) , | U | : M is the Euclidean norm of U , 2 = 2 n n - 2 is the critical Sobolev exponent, and...

Stabilization of monomial maps in higher codimension

Jan-Li Lin, Elizabeth Wulcan (2014)

Annales de l’institut Fourier

Similarity:

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 &gt; λ k - 1 λ k + 1 . On the other hand, we give examples of monomial maps f , where...

On small solutions of second order differential equations with random coefficients

László Hatvani, László Stachó (1998)

Archivum Mathematicum

Similarity:

We consider the equation x ' ' + a 2 ( t ) x = 0 , a ( t ) : = a k if t k - 1 t < t k , for k = 1 , 2 , ... , where { a k } is a given increasing sequence of positive numbers, and { t k } is chosen at random so that { t k - t k - 1 } are totally independent random variables uniformly distributed on interval [ 0 , 1 ] . We determine the probability of the event that all solutions of the equation tend to zero as t .

The n -th prime asymptotically

Juan Arias de Reyna, Jérémy Toulisse (2013)

Journal de Théorie des Nombres de Bordeaux

Similarity:

A new derivation of the classic asymptotic expansion of the n -th prime is presented. A fast algorithm for the computation of its terms is also given, which will be an improvement of that by Salvy (1994). Realistic bounds for the error with li - 1 ( n ) , after having retained the first m terms, for 1 m 11 , are given. Finally, assuming the Riemann Hypothesis, we give estimations of the best possible r 3 such that, for n r 3 , we have p n &gt; s 3 ( n ) where s 3 ( n ) is the sum of the first four terms of the asymptotic...

On Noether and strict stability, Hilbert exponent, and relative Nullstellensatz

Chia-chi Tung (2013)

Annales Polonici Mathematici

Similarity:

Conditions characterizing the membership of the ideal of a subvariety arising from (effective) divisors in a product complex space Y × X are given. For the algebra Y [ V ] of relative regular functions on an algebraic variety V, the strict stability is proved, in the case where Y is a normal space, and the Noether stability is established under a weakened condition. As a consequence (for both general and complete intersections) a global Nullstellensatz is derived for divisors in Y × N , respectively,...