71 citations · 484 across the 27 of their papers we have counts for
28 papers
Operon Dynamics with State Dependent Transcription and/or Translation Delays
Tomas Gedeon, Antony R. Humphries, Michael C. Mackey +3
Transcription and translation retrieve and operationalize gene encoded information in cells. These processes are not instantaneous and incur significant delays. In this paper we st…
How Can We Describe Density Evolution Under Delayed Dynamics?
Michael C. Mackey, Marta Tyran-Kamińska
Although the theory of density evolution in maps and ordinary differential equations is well developed, the situation is far from satisfactory in continuous time systems with delay…
Asymptotic (statistical) periodicity in two-dimensional maps
Fumihiko Nakamura, Michael C. Mackey
In this paper we give a new sufficient condition for asymptotic periodicity of Frobenius-Perron operator corresponding to two--dimensional maps. The result of the asymptotic period…
Randomly switching evolution equations
Paweł Klimasara, Michael C. Mackey, Andrzej Tomski +1
We present an investigation of stochastic evolution in which a family of evolution equations in are driven by continuous-time Markov processes. These are examples of so-calle…
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…
Response of an oscillatory delay differential equation to a periodic stimulus
Daniel C. De Souza, Michael C. Mackey
Periodic hematological diseases such as cyclical neutropenia or cyclical thrombocytopenia, with their characteristic oscillations of circulating neutrophils or platelets, may pose…