Convergence and stability for essentially strongly order-preserving semiflows

Generic Quasi-Convergence for Essentially Strongly Order-Preserving Semiflows

By employing the limit set dichotomy for essentially strongly order-preserving semiflows and the assumption that limit sets have infima and suprema in the state space, we prove a generic quasi-convergence principle implying the existence of an open and dense set of stable quasi-convergent points. We also apply this generic quasi-convergence principle to a model for biochemical feedback in prote...

Prevalent Behavior of Strongly Order Preserving Semiflows

Classical results in the theory of monotone semiflows give sufficient conditions for the generic solution to converge toward an equilibrium or towards the set of equilibria (quasiconvergence). In this paper, we provide new formulations of these results in terms of the measure-theoretic notion of prevalence, developed in [1, 8]. For monotone reaction-diffusion systems with Neumann boundary condi...

Generic Quasiconvergence for strongly order preserving semiflows: a new approach

The principal result of the theory of monotone semiflows says that for an open and dense set of initial data, the trajectory converges to the set of equilibria. We show that strong compactness assumptions on the semiflow, required for the proof, can be replaced by the assumption that limit sets have infimum and supremum in the space. This assumption is automatically satisfied in nice subsets of...

Convergence Theorems and Stability Results for Lipschitz Strongly Pseudocontractive Operators

Linear maps preserving or strongly preserving majorization on matrices

For $A,Bin M_{nm},$ we say that $A$ is left matrix majorized (resp. left matrix submajorized) by $B$ and write $Aprec_{ell}B$ (resp. $Aprec_{ell s}B$), if $A=RB$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $R.$ Moreover, we define the relation $sim_{ell s} $ on $M_{nm}$ as follows: $Asim_{ell s} B$ if $Aprec_{ell s} Bprec_{ell s} A.$ This paper characterizes all linear p...