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Global asymptotic stability for half-linear differential systems with coefficients of indefinite sign

Jitsuro Sugie, Masakazu Onitsuka (2008)

Archivum Mathematicum

This paper is concerned with the global asymptotic stability of the zero solution of the half-linear differential system x ' = - e ( t ) x + f ( t ) φ p * ( y ) , y ' = - g ( t ) φ p ( x ) - h ( t ) y , where p > 1 , p * > 1 ( 1 / p + 1 / p * = 1 ), and φ q ( z ) = | z | q - 2 z for q = p or q = p * . The coefficients are not assumed to be positive. This system includes the linear differential system 𝐱 ' = A ( t ) 𝐱 with A ( t ) being a 2 × 2 matrix as a special case. Our results are new even in the linear case ( p = p * = 2 ). Our results also answer the question whether the zero solution of the linear system is asymptotically stable even when Coppel’s condition does not hold...

Global attractor of a differentiable autonomous system on the plane

Nguyen Van Chau (1995)

Annales Polonici Mathematici

We study the structure of a differentiable autonomous system on the plane with non-positive divergence outside a bounded set. It is shown that under certain conditions such a system has a global attractor. The main result here can be seen as an improvement of the results of Olech and Meisters in [7,9] concerning the global asymptotic stability conjecture of Markus and Yamabe and the Jacobian Conjecture.

Global exponential stability of positive periodic solutions for an epidemic model with saturated treatment

Bingwen Liu (2016)

Annales Polonici Mathematici

This paper is concerned with an SIR model with periodic incidence rate and saturated treatment function. Under proper conditions, we employ a novel argument to establish a criterion on the global exponential stability of positive periodic solutions for this model. The result obtained improves and supplements existing ones. We also use numerical simulations to illustrate our theoretical results.

Global stability of steady solutions for a model in virus dynamics

Hermano Frid, Pierre-Emmanuel Jabin, Benoît Perthame (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical...

Global Stability of Steady Solutions for a Model in Virus Dynamics

Hermano Frid, Pierre-Emmanuel Jabin, Benoît Perthame (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical...

Currently displaying 321 – 340 of 930