Otwarty dostęp

With Andrzej Lasota There and Back Again


Zacytuj

J. Auslander and J.A. Yorke, Interval maps, factors of maps and chaos, Tohoku Math. J. (2) 32 (1980), 177–188. Search in Google Scholar

A. Bobrowski, T. Lipniacki, K. Pichór, and R. Rudnicki, Asymptotic behavior of distributions of mRNA and protein levels in a model of stochastic gene expression, J. Math. Anal. Appl. 333 (2007), 753–769. Search in Google Scholar

A. Bobrowski and R. Rudnicki, On convergence and asymptotic behaviour of semi-groups of operators, Philos. Trans. Roy. Soc. A 378 (2020), 20190613, 18 pp. Search in Google Scholar

F. Comets, S. Popov, G.M. Schütz, and M. Vachkovskaia, Billiards in a general domain with random reflections, Arch. Ration. Mech. Anal. 191 (2009), 497–537. Search in Google Scholar

M.H.A. Davis, Piecewise-deterministic Markov processes: a general class of nondiffusion stochastic models, J. Roy. Statist. Soc. Ser. B 46 (1984), 353–388. Search in Google Scholar

R.L. Devaney, An Introduction to Chaotic Dynamical Systems, 2nd ed., Addison-Wesley Stud. Nonlinearity, Addison-Wesley Publishing Company, Redwood City, CA, 1989. Search in Google Scholar

H.M. Hilden and L.J. Wallen, Some cyclic and non-cyclic vectors of certain operators, Indiana Univ. Math. J. 23 (1974), 557–565. Search in Google Scholar

A. Lasota, Invariant measures and a linear model of turbulence, Rend. Sem. Mat. Univ. Padova 61 (1979), 40–48. Search in Google Scholar

A. Lasota, Stable and chaotic solutions of a first order partial differential equation, Nonlinear Anal. 5 (1981), 1181–1193. Search in Google Scholar

A. Lasota, Asymptotic stability of some nonlinear Boltzmann-type equations, J. Math. Anal. Appl. 268 (2002), 291–309. Search in Google Scholar

A. Lasota and M.C. Mackey, Chaos, Fractals and Noise. Stochastic Aspects of Dynamics, Appl. Math. Sci., 97, Springer-Verlag, New York, 1994. Search in Google Scholar

A. Lasota and R. Rudnicki, Asymptotic behaviour of semigroups of positive operators on C(X), Bull. Polish Acad. Sci. Math. 36 (1988), 151–159. Search in Google Scholar

A. Lasota and J. Yorke, On the existence of invariant measures for piecewise monotonic transformations, Trans. Amer. Math. Soc. 186 (1973), 481–488. Search in Google Scholar

A. Lasota and J. Yorke, On the existence of invariant measures for transformations with strictly turbulent trajectories, Bull. Polish Acad. Sci. Math. 25 (1977), 233–238. Search in Google Scholar

A. Lasota and J. Yorke, Exact dynamical systems and the Frobenius–Perron operator, Trans. Amer. Math. Soc. 273 (1982), 375–384. Search in Google Scholar

A. Lasota and J. Yorke, When the long time behavior is independent of the initial density, SIAM J. Math. Anal. 27 (1996), 221–240. Search in Google Scholar

B. Lods, M. Mokhtar-Kharroubi, and R. Rudnicki, Invariant density and time asymptotics for collisionless kinetic equations with partly diffuse boundary operators, Ann. Inst. H. Poincaré C Anal. Non Linéaire 37 (2020), 877–923. Search in Google Scholar

M.C. Mackey and R. Rudnicki, Asymptotic similarity and Malthusian growth in autonomous and nonautonomous populations, J. Math. Anal. Appl. 187 (1994), 548–566. Search in Google Scholar

M.C. Mackey and R. Rudnicki, A new criterion for global stability of cell simultaneous cell replication and maturation processes, J. Math. Biol. 38 (1999), 195–219. Search in Google Scholar

M. Mokhtar-Kharroubi and R. Rudnicki, On asymptotic stability and sweeping of collisionless kinetic equations, Acta Appl. Math. 147 (2017), 19–38. Search in Google Scholar

G. Pianigiani and J.A. Yorke, Expanding maps on sets which are almost invariant: decay and chaos, Trans. Amer. Math. Soc. 252 (1979), 351–366. Search in Google Scholar

K. Pichór and R. Rudnicki, Continuous Markov semigroups and stability of transport equations, J. Math. Anal. Appl. 249 (2000), 668–685. Search in Google Scholar

K. Pichór and R. Rudnicki, Asymptotic decomposition of substochastic operators and semigroups, J. Math. Anal. Appl. 436 (2016), 305–321. Search in Google Scholar

K. Pichór and R. Rudnicki, Asymptotic decomposition of substochastic semigroups and applications, Stoch. Dyn. 18 (2018), 1850001, 18 pp. Search in Google Scholar

K. Pichór and R. Rudnicki, Stability of stochastic semigroups and applications to Stein’s neuronal model, Discrete Contin. Dyn. Syst. Ser. B 23 (2018), 377–385. Search in Google Scholar

K. Pichór and R. Rudnicki, Applications of stochastic semigroups to cell cycle models, Discrete Contin. Dyn. Syst. Ser. B 24 (2019), 2365–2381. Search in Google Scholar

K. Pichór and R. Rudnicki, Dynamics of antibody levels: asymptotic properties, Math. Methods Appl. Sci. 43 (2020), 10490–10499. Search in Google Scholar

K. Pichór and R. Rudnicki, Cell cycle length and long-time behavior of an age-size model, Math. Methods Appl. Sci. 45 (2022), 5797–5820. Search in Google Scholar

K. Pichór and R. Rudnicki, Asymptotic properties of a general model of immune status, SIAM J. Appl. Math. 83 (2023), 172–193. Search in Google Scholar

R. Rudnicki, Invariant measures for the flow of a first order partial differential equation, Ergodic Theory Dynam. Systems 5 (1985), 437–443. Search in Google Scholar

R. Rudnicki, Asymptotic properties of the iterates of positive operators on C(X), Bull. Polish Acad. Sci. Math. 34 (1986), 181–187. Search in Google Scholar

R. Rudnicki, Strong ergodic properties of a first-order partial differential equation, J. Math. Anal. Appl. 133 (1988), 14–26. Search in Google Scholar

R. Rudnicki, On asymptotic stability and sweeping for Markov operators, Bull. Polish Acad. Sci. Math. 43 (1995), 245–262. Search in Google Scholar

R. Rudnicki, Chaos for some infinite-dimensional dynamical systems, Math. Methods Appl. Sci. 27 (2004), 723–738. Search in Google Scholar

R. Rudnicki, Chaoticity of the blood cell production system, Chaos 19 (2009), 043112, 6 pp. Search in Google Scholar

R. Rudnicki, Chaoticity and invariant measures for a cell population model, J. Math. Anal. Appl. 393 (2012), 151–165. Search in Google Scholar

R. Rudnicki, An ergodic theory approach to chaos, Discrete Contin. Dyn. Syst. 35 (2015), 757–770. Search in Google Scholar

R. Rudnicki, 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.) Search in Google Scholar

R. Rudnicki, Ergodic properties of a semilinear partial differential equation, J. Differential Equations 372 (2023), 235–253. Search in Google Scholar

R. Rudnicki and A. Tomski, On a stochastic gene expression with pre-mRNA, mRNA and protein contribution, J. Theoret. Biol. 387 (2015), 54–67. Search in Google Scholar

R. Rudnicki and M. Tyran-Kamińska, Piecewise Deterministic Processes in Biological Models, SpringerBriefs Appl. Sci. Technol., Math. Methods, Springer, Cham, 2017. Search in Google Scholar

R. Rudnicki and P. Zwoleński, Model of phenotypic evolution in hermaphroditic populations, J. Math. Biol. 70 (2015), 1295–1321. Search in Google Scholar

eISSN:
2391-4238
Język:
Angielski
Częstotliwość wydawania:
2 razy w roku
Dziedziny czasopisma:
Mathematics, General Mathematics