Ryszard Rudnicki – List of publications
Journal articles:
Electronic files of articles can be found at the Research Gate
- Invariant measures for the flow of a first order partial differential
equation, Ergodic Theory Dynamical Systems, 5 (1985), 437-443.
- Ergodic properties of hyperbolic systems of partial differential
equations, Bull. Polish Acad. Sci. Math., 33 (1985), 595-599.
- Asymptotic properties of the iterates of positive operators on C(X),
Bull. Polish Acad. Sci. Math., 34 (1986), 181-187.
- An abstract Wiener measure invariant under a partial
differential equation, Bull. Polish Acad. Sci. Math., 35 (1987), 289-295.
- with A. Lasota, Asymptotic behaviour of semigroups of positive
operators on C(X), Bull. Polish Acad. Sci. Math., 36 (1988), 151-159.
- Periods of slowly oscillating solutions of first order delay differential
equations, Univ. Iagell. Ac. Math., 26 (1987), 227-230.
- Ergodic measures on topological spaces,
Univ. Iagell. Ac. Math., 26 (1987), 231-237.
- Strong ergodic properties of a first-order
partial differential equation, J. Math. Anal. Appl., 133 (1988), 14-26.
- Stability of iterates of Markov operators,
Ann. Pol. Math., 48 (1988), 95-104.
- with K. Łoskot, Sweeping of some integral operators,
Bull. Polish Acad. Sci. Math., 37 (1989), 229-235.
- with K. Łoskot, Mixing and some
integro-functional equations, Aequationes Math., 40, (1990) 78-82.
- with A. Kamiński,
A note on the convolution and the product in D˘ and S˘,
Internat. J. Math. Math. Sci., 14 (1991), 275-282.
- with K. Łoskot,
Relative entropy and stability of stochastic semigroups, Ann. Pol. Math.,
53 (1991), 139-145.
- On a one-dimensional analogue of the Smale horseshoe,
Ann. Pol. Math., 54 (1991), 147-153.
- Asymptotic behaviour of a transport equation,
Ann. Pol. Math., 57 (1992), 45-55.
- Asymptotic behaviour of an integro-parabolic equation,
Bull. Polish Acad. Sci. Math., 40 (1992), 111-128.
- Strangely sweeping one-dimensional diffusion,
Ann. Pol. Math., 58 (1993), 37-45.
- Asymptotical stability in L1 of parabolic equations,
J. Diff. Eq., 102 (1993), 391-401.
- Gaussian measure-preserving linear transformations,
Univ. Iagell. Ac. Math., 30 (1993), 105-112.
- with M. C. Mackey, Asymptotic similarity and
Malthusian growth in autonomous and nonautonomous populations, J. Math. Anal. Appl., 187 (1994), 548-566.
- with M. C. Mackey,
Global stability in a delayed partial differential equation describing cellular
replication, J. Math. Biol., 33 (1994), 89-109.
- On composition of functions and measures,
in: Different aspects of differentiability, D.Przeworska-Rolewicz (ed.),
Dissertationes Mathematicae, 340 (1995), 309-320.
- with K. Łoskot,
Limit theorems for stochastically perturbed dynamical systems, J. App. Prob.,
32 (1995), 459-469.
- Asymptotic properties of the Fokker-Planck equation,
in: Chaos: The interplay between stochastics and deterministic behaviour,
Karpacz'95 Proc., P. Garbaczewski, M. Wolf, A. Weron eds., Lecture Notes in
Physics, vol. 457, Springer, Berlin 1995, 517-521.
- On asymptotic stability and sweeping for Markov operators,
Bull. Polish Acad. Sci. Math., 43 (1995), 245-262.
- Stability in L1 of some integral operators,
Integ. Equat. Oper. Th., 24 (1996), 320-327.
- with J. Łuczka, Randomly
flashing diffusion: asymptotic properties, J. Statis. Phys., 83 (1996),
1149-1164.
- with J. Łuczka, Long-time asymptotics for diffusing clusters with
Poisson growth statistics, Fractals 4 (1996), 543-546.
- Asymptotic stability of Markov operators: a
counter-example, Bull. Polish Acad. Sci. Math., 45 (1997), 1-5.
- Generic properties of multiplicative functions and
stochastic semigroups, Bull. Polish Acad. Sci. Math., 45 (1997), 7-16.
- Global stability of a nonlinear model of cellular
populations, J. Tech. Phys., 38 (1997), 333-336.
- with K. Pichór,
Stability of Markov semigroups and applications to parabolic systems, J.
Math. Anal. Appl., 215 (1997), 56-74.
- with K. Pichór, Asymptotic behaviour of Markov
semigroups and applications to transport equations, Bull. Polish Acad. Sci.
Math., 45 (1997), 379-397.
- with K. Łoskot and A. Polański,
Further comments on vector norms as Lyapunov functions for linear systems,
IEEE Trans. Autom. Control, 43 (1998), 289-291.
- with M. C. Mackey,
A new criterion for global stability of cell simultaneous cell replication
and maturation processes, J. Math. Biol., 38 (1999), 195-219.
- with M. Wolf, Random walk with memory,
J. Math. Phys., 40 (1999), 3072-3083.
- Markov operators: applications to
diffusion processes and population dynamics, Applicationes Mathematicae, 27
(2000), 67-79.
- Strong and weak stability of some Markov operators,
Colloq. Math., 84-85 (2000), 255-263.
- with K. Pichór,
Markov semigroups and stability of the cell maturity distribution, J. Biol.
Systems 8 (2000), 69-94.
- with K. Pichór, Continuous Markov semigroups and
stability of transport equations, J. Math. Anal. Appl., 249 (2000),
668-685.
- with J. Myjak,
Box and packing dimensions of typical compact sets, Monatsh. Math. 131
(2000), 223-226.
- with C. Heurie, D. C. Dale and M. C. Mackey,
Modeling complex neutrophil dynamics in the Grey Collie, J. Theor. Biol.
204 (2000), 505-519.
- with L. Pujo-Menjouet,
Global stability of cellular populations with unequal division, Canad. Appl. Math. Quart. 8 (2000), 185-202.
- with J. Myjak, On the typical structure of compact
sets, Arch. Math. 76 (2001), 119-126.
- Pointwise dimensions and Rényi dimensions,
Proc. Amer. Math. Soc. 130 (2002), 1981-1982.
- with J. Myjak,
On the box dimension of typical measures, Monatsh. Math. 136 (2002),
143-150.
- with J. Myjak,
Stability versus chaos for a partial differential equation, Chaos Solitons
and Fractals, 14 (2002), 607-612.
- with K. Pichór and M. Tyran-Kamińska,
Markov semigroups and their applications, in Dynamics of Dissipation, P.
Garbaczewski and R. Olkiewicz (eds.), Lecture Notes in Physics, vol. 597,
Springer, Berlin 2002, 215-238.
- with J. Łuczka and M. Niemiec, Kinetics of growth process controlled by
convective fluctuations, Phys. Rev. E 65 (2002), 051401-9.
- with J. Myjak,
Typical properties of correlation dimension, Real Anal. Exchange 28
(2002/2003), 269-278.
- Long-time behaviour of a stochastic prey-predator model,
Stoch. Processes Appl. 108 (2003), 93-107.
- with A. Gadomski and J. Łuczka, Finite volume effects in a model grain growth,
Physica A 325 (2003), 284-291.
- Chaos for some infinite-dimensional dynamical systems
Math. Meth. Appl. Sci.27 (2004), 723-738.
- with O. Arino, Phytoplankton dynamics,
Comptes Rendus Biologies, 327 (11) (2004), 961-969.
- with J. Tiuryn and D. Wojtowicz,
A case study of genome evolution: from continuous to discrete time model,
in: Proceedings of 29th International Symposium, MFCS 2004, Prague, Czech
Republic, August 22-27, 2004, Jirí Fiala, Václav Koubek, Jan Kratochvíl (eds.),
Lecture Notes in Computer Science, vol. 3153, Springer, Heidelberg 2004,
1-24.
- with P. Hänggi and J. Łuczka, The diffusion in the quantum
Smoluchowski equation, Physica A, 351 (2005), 60-68.
- with W.T. Mocek, E.O. Voit,
Approximation of delays in biochemical systems, Mathematical Biosciences
198 (2005), 190-216.
- with R. Wieczorek, Fragmentation - coagulation models of phytoplankton,
Bull. Pol. Acad. Sci. Math. 54 (2006), 175-191.
- with K. Nishimura and J. Stachurski, Stochastic optimal growth with
nonconvexities, J. Math. Economics 42 (2006), 74-96.
- with J. Tiuryn and D. Wójtowicz, A model for the evolution of paralog families in genomes,
J. Math. Biology 53 (2006), 759-770.
- with R. Wieczorek,
Phytoplankton dynamics: from the behaviour of cells to a transport equation,
Mathematical Modelling of Natural Phenomena 1 (2006), 83-100.
- with K. Pichór, Influence of stochastic
perturbation on prey-predator systems, Mathematical Biosciences 206
(2007), 108-119.
- with A. Bobrowski, T. Lipniacki, K. Pichór,
Asymptotic behavior of distributions of mRNA and protein levels in a model of
stochastic gene expression, J. Math. Anal. Appl. 333 (2007), 753-769.
- with J. Myjak, On the information dimensions,
Bolletino UMI 10 (2007), 357-364.
- with J. Tiuryn and D. Wojtowicz, A model of evolution of small paralog families in genomes,
Mathematical Models and Methods in Applied Sciences 17 (2007), 933-955.
- with J. Myjak, Reinforced walk on graphs and neural networks,
Studia Math. 189 (2008), 255-268.
- with R. Wieczorek,
Mathematical models of phytoplankton dynamics,
in: Russo R. (ed.) Aquaculture I. Dynamic Biochemistry, Process Biotechnology and Molecular Biology 2 (Special Issue 1), (2008) 55-63.
- with R. Wieczorek,
Can mathematics solve biological riddles? The World in Equations,
also Polish version: Czy matematyka może rozwiązać biologiczne zagadki? Świat w równaniach, Academia 1 (21) 2009, 20-23.
-
Models of population dynamics and their applications in genetics,
in: From Genetics to Mathematics, M. Lachowicz and J. Miękisz (eds.),
Series on Advances in Mathematics for Applied Sciences, Vol. 79,
World Scientific Publications, New Jersey 2009, pp. 103-147.
-
Chaoticity of the blood cell production system,
Chaos: An Interdisciplinary Journal of Nonlinear Science, 19 (2009), 043112, 1-6.
-
with J. Banasiak, S. C. Oukouomi Noutchie,
Global solvability of a fragmentation-coagulation equation with growth and restricted coagulation,
Journal of Nonlinear Mathematical Physics 16 (2009), 13-26.
-
with R. Wieczorek, Asymptotic analysis of a semelparous species model,
Fundamenta Informaticae 103 (2010), 219-233.
- with J. Banasiak, K. Pichór,
Asynchronous exponential growth of a general structured population model,
Acta Applicandae Mathematicae 119 (2012), 149-166.
-
Chaoticity and invariant measures for a cell population model, J. Math. Anal. Appl. 393 (2012), 151-165.
-
with K. Pichór and M. Tyran-Kamińska,
Stochastic semigroups and their applications to biological models,
Demonstratio Mathematica 45 (2012), 463-494.
-
with J. Tiuryn, Size distribution of gene families in a genome, Math. Models Methods Appl. Sci.
24 (2014), 697-717.
- with R. Wieczorek, On a nonlinear age-structured model of semelparous species,
Discrete Contin. Dyn. Syst. B 19 (2014), 2641-2656.
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An ergodic theory approach to chaos, Discrete Contin. Dyn. Syst. A 35 (2015), 757-770.
-
with M. Tyran-Kamińska, Piecewise deterministic Markov processes in biological models,
in J. Banasiak et al. (eds.), Semigroups of Operators - Theory and Applications,
Springer Proceedings in Mathematics & Statistics Vol. 113 (2015), 235-255.
- Stochastic operators and semigroups and their applications in physics and biology,
in J. Banasiak, M. Mokhtar-Kharroubi (eds.), Evolutionary Equations
with Applications in Natural Sciences, Lecture Notes in Mathematics 2126 (2015), 255-318.
-
with P. Zwoleński, Model of phenotypic evolution in hermaphroditic populations,
J. Math. Biol. 70 (2015), 1295-1321.
-
with A. Tomski, On a stochastic gene expression with pre-mRNA, mRNA and protein contribution,
J. Theor. Biology 387 (2015), 54-67.
-
with K. Pichór, Asymptotic decomposition of substochastic operators and semigroups, J. Math. Anal. Appl. 436 (2016), 305-321.
- with Mokhtar-Kharroubi, On asymptotic stability and sweeping of collisionless kinetic equations, Acta Appl. Math. 147 (2017) 19-38.
- with K. Argasinski, Nest site lottery revisited. Towards the mechanistic model of population growth suppressed by availability of nest sites,
J. Theor. Biology 420 (2017), 279-289.
- Does a population with the highest turnover coefficient win competition?, Journal of Difference Equations and Applications 23 (2017), 1529-1541.
- with K. Pichór, Asymptotic decomposition of substochastic semigroups and applications, Stochastics and Dynamics 18 (2018), 1850001 (18 pages).
- with K. Pichór, Stability of stochastic semigroups and applications to Stein's neuronal model, Discrete Contin. Dyn. Syst. B 23 (2018), 377-385.
- with R. Wieczorek, Does assortative mating lead to a polymorphic population? A toy model justification, Discrete Contin. Dyn. Syst. B 23 (2018), 459-472.
Books:
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Lectures on Mathematical Analysis (in Polish), PWN,
Warszawa, 2001, 2002.
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Models and Methods Mathematical Biology. Part I: Deterministic Models, (in Polish), Księgozbiór Matematyczny 2,
IMPAN, Warszawa 2014. (Modele i Metody Biologii Matematycznej, Część I: Modele deterministyczne).
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with M. Tyran-Kamińska, Piecewise Deterministic Processes in Biological Models, SpringerBriefs in Applied Sciences and Technology, Mathematical Methods, Springer,
Cham, Switzerland 2017.
Editor of volumes:
- (with Ovide Arino and Pierre Auger) Mathematical Modelling of
Population Dynamics, Będlewo Conference, Poland, 24-28 June, 2002, Comptes
Rendus Biologies, Vol 327 (3) (2004).
- Mathematical Modelling of Population Dynamics, Banach Center
Publications, Vol 63, Warszawa 2004.
- (with Marek Kimmel and Eva Sanches), A special volume in memory of Ovide
Arino, Mathematical Biosciences.
Katowice, February 2018
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