Ryszard Rudnicki – List of publications

Journal articles:

Electronic files of articles can be found at the Research Gate

  1. Invariant measures for the flow of a first order partial differential equation, Ergodic Theory Dynamical Systems, 5 (1985), 437-443.
  2. Ergodic properties of hyperbolic systems of partial differential equations, Bull. Polish Acad. Sci. Math., 33 (1985), 595-599.
  3. Asymptotic properties of the iterates of positive operators on C(X), Bull. Polish Acad. Sci. Math., 34 (1986), 181-187.
  4. An abstract Wiener measure invariant under a partial differential equation, Bull. Polish Acad. Sci. Math., 35 (1987), 289-295.
  5. with A. Lasota, Asymptotic behaviour of semigroups of positive operators on C(X), Bull. Polish Acad. Sci. Math., 36 (1988), 151-159.
  6. Periods of slowly oscillating solutions of first order delay differential equations, Univ. Iagell. Ac. Math., 26 (1987), 227-230.
  7. Ergodic measures on topological spaces, Univ. Iagell. Ac. Math., 26 (1987), 231-237.
  8. Strong ergodic properties of a first-order partial differential equation, J. Math. Anal. Appl., 133 (1988), 14-26.
  9. Stability of iterates of Markov operators, Ann. Pol. Math., 48 (1988), 95-104.
  10. with K. Łoskot, Sweeping of some integral operators, Bull. Polish Acad. Sci. Math., 37 (1989), 229-235.
  11. with K. Łoskot, Mixing and some integro-functional equations, Aequationes Math., 40, (1990) 78-82.
  12. with A. Kamiński, A note on the convolution and the product in D˘ and S˘, Internat. J. Math. Math. Sci., 14 (1991), 275-282.
  13. with K. Łoskot, Relative entropy and stability of stochastic semigroups, Ann. Pol. Math., 53 (1991), 139-145.
  14. On a one-dimensional analogue of the Smale horseshoe, Ann. Pol. Math., 54 (1991), 147-153.
  15. Asymptotic behaviour of a transport equation, Ann. Pol. Math., 57 (1992), 45-55.
  16. Asymptotic behaviour of an integro-parabolic equation, Bull. Polish Acad. Sci. Math., 40 (1992), 111-128.
  17. Strangely sweeping one-dimensional diffusion, Ann. Pol. Math., 58 (1993), 37-45.
  18. Asymptotical stability in L1 of parabolic equations, J. Diff. Eq., 102 (1993), 391-401.
  19. Gaussian measure-preserving linear transformations, Univ. Iagell. Ac. Math., 30 (1993), 105-112.
  20. with M. C. Mackey, Asymptotic similarity and Malthusian growth in autonomous and nonautonomous populations, J. Math. Anal. Appl., 187 (1994), 548-566.
  21. with M. C. Mackey, Global stability in a delayed partial differential equation describing cellular replication, J. Math. Biol., 33 (1994), 89-109.
  22. On composition of functions and measures, in: Different aspects of differentiability, D.Przeworska-Rolewicz (ed.), Dissertationes Mathematicae, 340 (1995), 309-320.
  23. with K. Łoskot, Limit theorems for stochastically perturbed dynamical systems, J. App. Prob., 32 (1995), 459-469.
  24. 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.
  25. On asymptotic stability and sweeping for Markov operators, Bull. Polish Acad. Sci. Math., 43 (1995), 245-262.
  26. Stability in L1 of some integral operators, Integ. Equat. Oper. Th., 24 (1996), 320-327.
  27. with J. Łuczka, Randomly flashing diffusion: asymptotic properties, J. Statis. Phys., 83 (1996), 1149-1164.
  28. with J. Łuczka, Long-time asymptotics for diffusing clusters with Poisson growth statistics, Fractals 4 (1996), 543-546.
  29. Asymptotic stability of Markov operators: a counter-example, Bull. Polish Acad. Sci. Math., 45 (1997), 1-5.
  30. Generic properties of multiplicative functions and stochastic semigroups, Bull. Polish Acad. Sci. Math., 45 (1997), 7-16.
  31. Global stability of a nonlinear model of cellular populations, J. Tech. Phys., 38 (1997), 333-336.
  32. with K. Pichór, Stability of Markov semigroups and applications to parabolic systems, J. Math. Anal. Appl., 215 (1997), 56-74.
  33. with K. Pichór, Asymptotic behaviour of Markov semigroups and applications to transport equations, Bull. Polish Acad. Sci. Math., 45 (1997), 379-397.
  34. 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.
  35. 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.
  36. with M. Wolf, Random walk with memory, J. Math. Phys., 40 (1999), 3072-3083.
  37. Markov operators: applications to diffusion processes and population dynamics, Applicationes Mathematicae, 27 (2000), 67-79.
  38. Strong and weak stability of some Markov operators, Colloq. Math., 84-85 (2000), 255-263.
  39. with K. Pichór, Markov semigroups and stability of the cell maturity distribution, J. Biol. Systems 8 (2000), 69-94.
  40. with K. Pichór, Continuous Markov semigroups and stability of transport equations, J. Math. Anal. Appl., 249 (2000), 668-685.
  41. with J. Myjak, Box and packing dimensions of typical compact sets, Monatsh. Math. 131 (2000), 223-226.
  42. 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.
  43. with L. Pujo-Menjouet, Global stability of cellular populations with unequal division, Canad. Appl. Math. Quart. 8 (2000), 185-202.
  44. with J. Myjak, On the typical structure of compact sets, Arch. Math. 76 (2001), 119-126.
  45. Pointwise dimensions and Rényi dimensions, Proc. Amer. Math. Soc. 130 (2002), 1981-1982.
  46. with J. Myjak, On the box dimension of typical measures, Monatsh. Math. 136 (2002), 143-150.
  47. with J. Myjak, Stability versus chaos for a partial differential equation, Chaos Solitons and Fractals, 14 (2002), 607-612.
  48. 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.
  49. with J. Łuczka and M. Niemiec, Kinetics of growth process controlled by convective fluctuations, Phys. Rev. E 65 (2002), 051401-9.
  50. with J. Myjak, Typical properties of correlation dimension, Real Anal. Exchange 28 (2002/2003), 269-278.
  51. Long-time behaviour of a stochastic prey-predator model, Stoch. Processes Appl. 108 (2003), 93-107.
  52. with A. Gadomski and J. Łuczka, Finite volume effects in a model grain growth, Physica A 325 (2003), 284-291.
  53. Chaos for some infinite-dimensional dynamical systems Math. Meth. Appl. Sci.27 (2004), 723-738.
  54. with O. Arino, Phytoplankton dynamics, Comptes Rendus Biologies, 327 (11) (2004), 961-969.
  55. 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.
  56. with P. Hänggi and J. Łuczka, The diffusion in the quantum Smoluchowski equation, Physica A, 351 (2005), 60-68.
  57. with W.T. Mocek, E.O. Voit, Approximation of delays in biochemical systems, Mathematical Biosciences 198 (2005), 190-216.
  58. with R. Wieczorek, Fragmentation - coagulation models of phytoplankton, Bull. Pol. Acad. Sci. Math. 54 (2006), 175-191.
  59. with K. Nishimura and J. Stachurski, Stochastic optimal growth with nonconvexities, J. Math. Economics 42 (2006), 74-96.
  60. with J. Tiuryn and D. Wójtowicz, A model for the evolution of paralog families in genomes, J. Math. Biology 53 (2006), 759-770.
  61. with R. Wieczorek, Phytoplankton dynamics: from the behaviour of cells to a transport equation, Mathematical Modelling of Natural Phenomena 1 (2006), 83-100.
  62. with K. Pichór, Influence of stochastic perturbation on prey-predator systems, Mathematical Biosciences 206 (2007), 108-119.
  63. 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.
  64. with J. Myjak, On the information dimensions, Bolletino UMI 10 (2007), 357-364.
  65. 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.
  66. with J. Myjak, Reinforced walk on graphs and neural networks, Studia Math. 189 (2008), 255-268.
  67. 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.
  68. 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.
  69. 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.
  70. Chaoticity of the blood cell production system, Chaos: An Interdisciplinary Journal of Nonlinear Science, 19 (2009), 043112, 1-6.
  71. 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.
  72. with R. Wieczorek, Asymptotic analysis of a semelparous species model, Fundamenta Informaticae 103 (2010), 219-233.
  73. with J. Banasiak, K. Pichór, Asynchronous exponential growth of a general structured population model, Acta Applicandae Mathematicae 119 (2012), 149-166.
  74. Chaoticity and invariant measures for a cell population model, J. Math. Anal. Appl. 393 (2012), 151-165.
  75. with K. Pichór and M. Tyran-Kamińska, Stochastic semigroups and their applications to biological models, Demonstratio Mathematica 45 (2012), 463-494.
  76. with J. Tiuryn, Size distribution of gene families in a genome, Math. Models Methods Appl. Sci. 24 (2014), 697-717.
  77. with R. Wieczorek, On a nonlinear age-structured model of semelparous species, Discrete Contin. Dyn. Syst. B 19 (2014), 2641-2656.
  78. An ergodic theory approach to chaos, Discrete Contin. Dyn. Syst. A 35 (2015), 757-770.
  79. 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.
  80. 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.
  81. with P. Zwoleński, Model of phenotypic evolution in hermaphroditic populations, J. Math. Biol. 70 (2015), 1295-1321.
  82. with A. Tomski, On a stochastic gene expression with pre-mRNA, mRNA and protein contribution, J. Theor. Biology 387 (2015), 54-67.
  83. with K. Pichór, Asymptotic decomposition of substochastic operators and semigroups, J. Math. Anal. Appl. 436 (2016), 305-321.
  84. with Mokhtar-Kharroubi, On asymptotic stability and sweeping of collisionless kinetic equations, Acta Appl. Math. 147 (2017) 19-38.
  85. 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.
  86. Does a population with the highest turnover coefficient win competition?, Journal of Difference Equations and Applications 23 (2017), 1529-1541.
  87. with K. Pichór, Asymptotic decomposition of substochastic semigroups and applications, Stochastics and Dynamics 18 (2018), 1850001 (18 pages).
  88. with K. Pichór, Stability of stochastic semigroups and applications to Stein's neuronal model, Discrete Contin. Dyn. Syst. B 23 (2018), 377-385.
  89. with R. Wieczorek, Does assortative mating lead to a polymorphic population? A toy model justification, Discrete Contin. Dyn. Syst. B 23 (2018), 459-472.
  90. with K. Pichór, Applications of stochastic semigroups to cell cycle models, Discrete Contin. Dyn. Syst. B 24 (2019), 2365-2381.
  91. with K. Pichór, One and two-phase cell cycle models, Biomath 8 (2019), 1905261 (15 pages).
  92. with K. Argasiński, From Nest Site Lottery to Host Lottery: continuous model of growth suppression driven by availability of nest sites for newborns or hosts for parasites and its impact on selection of life history strategies, Theory Biosci. 139 (2020), 171-188.
  93. with B. Lods and M. Mokhtar-Kharroubi, Invariant density and time asymptotics for collisionless kinetic equations with partly diffuse boundary operators, Ann. I. H. Poincaré AN 37(2020), 877-923.
  94. with K. Pichór, Dynamics of antibody levels: Asymptotic properties, Math. Meth. Appl. Sci., 43 (2020); 10490-10499.
  95. with K. Pichór, Asymptotic properties of stochastic semigroups with applications to piecewise deterministic Markov processes, in J. Banasiak et. al. (eds.), Semigroups of Operators: Theory and Applications SOTA-2018, Springer Proceedings in Mathematics & Statistics Vol. 325 (2020), 329-347.
  96. with A. Bobrowski, On convergence and asymptotic behaviour of semigroups of operators, Phil. Trans. R. Soc. A. 378 (2020): 20190613 (18 pages).
  97. with K. Argasiński, Replicator dynamics for the game theoretic selection models based on state, J. Theoretical Biology, 526 (2021), 110540 (24 pages).
  98. with K. Pichór, Cell cycle length and long-time behavior of an age-size model, Math. Meth. Appl. Sci., 45 (2022), 5797-5820.
  99. with K. Pichór, Asymptotic properties of a general model of immune status, SIAM Journal on Applied Mathematics, 83 (2023), 172-193.
  100. Ergodic properties of a semilinear partial differential equation, Journal of Differential Equations, 372 (2023), 235-253.


  1. Lectures on Mathematical Analysis (in Polish), PWN, Warszawa, 2001, 2002, 2020 II edition (extended).
  2. 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).
  3. with M. Tyran-Kamińska, Piecewise Deterministic Processes in Biological Models, SpringerBriefs in Applied Sciences and Technology, Mathematical Methods, Springer, Cham, Switzerland 2017.
  4. Models and Methods Mathematical Biology. Part II: Probabilistic Models, (in Polish), Księgozbiór Matematyczny 4, IMPAN, Warszawa 2022. (Modele i Metody Biologii Matematycznej, Część II: Modele probabilistyczne).

Editor of volumes:

  1. (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).
  2. Mathematical Modelling of Population Dynamics, Banach Center Publications, Vol 63, Warszawa 2004.
  3. (with Marek Kimmel and Eva Sanches), A special volume in memory of Ovide Arino, Mathematical Biosciences.

Katowice, November 2023