58 citations · 395 across the 20 of their papers we have counts for
20 papers
Temporal Entropy Evolution in Stochastic and Delayed Dynamics
Michael C. Mackey, Marta Tyran-Kaminska
We review the behaviour of the Gibbs' and conditional entropies in deterministic and stochastic systems and continue to a formulation appropriate for a stochastically perturbed sys…
A model of seasonal savanna dynamics
Paweł Klimasara, Marta Tyran-Kamińska
We introduce a mathematical model of savanna vegetation dynamics. The usual approach of nonequilibrium ecology is extended by including the impact of wet and dry seasons. We presen…
Positive semigroups and perturbations of boundary conditions
Piotr Gwiżdż, Marta Tyran-Kamińska
We present a generation theorem for positive semigroups on an space. It provides sufficient conditions for the existence of positive and integrable solutions of initial-bound…
The combined effects of Feller diffusion and transcriptional/translational bursting in simple gene networks
Mateusz Falfus, Michael C. Mackey, Marta Tyran-Kaminska
We study a stochastic model of biosynthesis of proteins in generic bacterial operons. The stochasticity arises from two different processes, namely from `bursting' production of ei…
Self-similar solutions of fragmentation equations revisited
Weronika Biedrzycka, Marta Tyran-Kaminska
We study the large time behaviour of the mass (size) of particles described by the fragmentation equation with homogeneous breakup kernel. We give necessary and sufficient conditio…
Piecewise deterministic Markov processes in biological models
Ryszard Rudnicki, Marta Tyran-Kaminska
We present a short introduction into the framework of piecewise deterministic Markov processes. We illustrate the abstract mathematical setting with a series of examples related to…