25 citations · 133 across the 15 of their papers we have counts for
15 papers
Parabolic Differential Equations with Bounded Delay
Marek Kryspin, Janusz Mierczyński
We show the continuous dependence of solutions of linear nonautonomous second order parabolic partial differential equations (PDEs) with bounded delay on coefficients and delay. Th…
Existence of the carrying simplex for a retrotone map
Janusz Mierczyński, Stephen Baigent
We present a dynamical approach to the study of unordered, attracting manifolds of retrotone maps commonly known as carrying simplices. Our approach is novel in that it uses the ra…
Linearization and invariant manifolds on the carrying simplex for competitive maps
Janusz Mierczyński, Lei Niu, Alfonso Ruiz-Herrera
A folklore result due to M.W. Hirsch states that most competitive maps admit a carrying simplex, i.e., an invariant hypersurface which attracts all nontrivial orbits. The common ap…
Lyapunov exponents and Oseledets decomposition in random dynamical systems generated by systems of delay differential equations
Janusz Mierczyński, Sylvia Novo, Rafael Obaya
Linear skew-product semidynamical systems generated by random systems of delay differential equations are considered, both on a space of continuous functions as~well as on a space…
The property of convex carrying simplices for three-dimensional competitive maps
Janusz Mierczyński
It is proved that a convex carrying simplex for a three-dimensional competitive map is a submanifold-with-corners neatly embedded in the non-negative octant.
Globally positive solutions of linear parabolic partial differential equations of second order with Dirichlet boundary conditions
Janusz Mierczyński
It is shown that globally positive solutions of a linear second order parabolic partial differential equation on a bounded domain, with Dirichlet boundary conditions, are unique up…
Time averaging for nonautonomous/random linear parabolic equations
Janusz Mierczyński, Wenxian Shen
Linear nonautonomous/random parabolic partial differential equations are considered under the Dirichlet, Neumann or Robin boundary conditions, where both the zero order coefficient…
Globally positive solutions of linear parabolic PDE's of second order with Robin boundary conditions
Janusz Mierczyński
It is shown that globally positive solutions of a linear second order parabolic partial differential equation on a bounded domain, with Robin boundary conditions, are unique up to…
On smoothness of carrying simplices
Janusz Mierczyński
We consider dissipative strongly competitive systems of ordinary differential equations. It is known that for a wide class of such systems there exists…
Principal Floquet subspaces and exponential separations of type II with applications to random delay differential equations
Janusz Mierczyński, Sylvia Novo, Rafael Obaya
This paper deals with the study of principal Lyapunov exponents, principal Floquet subspaces, and exponential separation for positive random linear dynamical systems in ordered Ban…
Formulas for generalized principal Lyapunov exponent for parabolic PDEs
Janusz Mierczyński, Wenxian Shen
An integral formula is given representing the generalized principal Lyapunov estimate for random linear parabolic PDEs. As an application, an upper estimate of the exponent is obta…
Averaging in random systems of nonnegative matrices
Janusz Mierczyński
It is proved that for the top Lyapunov exponent of a random matrix system of the form , where is a nonnegative matrix and is a diagonal matrix with positive…
Lower estimates of top Lyapunov exponent for cooperative random systems of linear ODEs
Janusz Mierczyński
For cooperative random linear systems of ordinary differential equations a method is presented of obtaining lower estimates of the top Lyapunov exponent. The proofs are based on ap…
Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. I. General theory
Janusz Mierczyński, Wenxian Shen
This is the first of a series of papers concerned with principal Lyapunov exponents and principal Floquet subspaces of positive random dynamical systems in ordered Banach spaces. I…
Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. II. Finite-dimensional systems
Janusz Mierczyński, Wenxian Shen
This is the second part in a series of papers concerned with principal Lyapunov exponents and principal Floquet subspaces of positive random dynamical systems in ordered Banach spa…