19 citations · 57 across the 5 of their papers we have counts for
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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…
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…