Zobrazeno 1 - 10
of 377
pro vyhledávání: '"Mackey, Michael C."'
We present a detailed study of a scalar differential equation with threshold state-dependent delayed feedback. This equation arises as a simplification of a gene regulatory model. There are two monotone nonlinearities in the model: one describes the
Externí odkaz:
http://arxiv.org/abs/2410.13092
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 system with delayed dynamics. The underlying question driving these inves
Externí odkaz:
http://arxiv.org/abs/2311.16800
Publikováno v:
J. Math. Biol. 84, 2 (2022)
Transcription and translation retrieve and operationalize gene encoded information in cells. These processes are not instantaneous and incur significant delays. In this paper we study Goodwin models of both inducible and repressible operons with stat
Externí odkaz:
http://arxiv.org/abs/2106.06628
Publikováno v:
Chaos 31, 043114 (2021)
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. This paper reviews some of the work that has been done numerically a
Externí odkaz:
http://arxiv.org/abs/2011.14643
Autor:
Nakamura, Fumihiko, Mackey, Michael C.
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 periodicity for strictly expanding systems, that is, all eigenvalues of the
Externí odkaz:
http://arxiv.org/abs/2011.10689
Publikováno v:
Nonlinear Analysis: Hybrid Systems 39 (2021) 100948
We present an investigation of stochastic evolution in which a family of evolution equations in $L^1$ are driven by continuous-time Markov processes. These are examples of so-called piecewise deterministic Markov processes (PDMP's) on the space of in
Externí odkaz:
http://arxiv.org/abs/2009.04764
Publikováno v:
Journal of Mathematical Analysis and Applications 470 (2019), 931-953
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 either mRNA and/or protein (in the transcription/translation process) an
Externí odkaz:
http://arxiv.org/abs/1805.12056
Periodic hematological diseases such as cyclical neutropenia or cyclical thrombocytopenia, with their characteristic oscillations of circulating neutrophils or platelets, may pose grave problems for patients. Likewise, periodically administered chemo
Externí odkaz:
http://arxiv.org/abs/1805.05434
Autor:
Langlois, Gabriel P., Craig, Morgan, Humphries, Antony R., Mackey, Michael C., Mahaffy, Joseph M., Bélair, Jacques, Moulin, Thibault, Sinclair, Sean R., Wang, Liangliang
Publikováno v:
Journal of Mathematical Biology volume 75, pages 1411-1462 (2017)
We develop a comprehensive mathematical model of platelet, megakaryocyte, and thrombopoietin dynamics in humans. We show that there is a single stationary solution that can undergo a Hopf bifurcation, and use this information to investigate both norm
Externí odkaz:
http://arxiv.org/abs/1608.02806