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Stability and chaotic properties of multidimensional Lasota equation

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Języki publikacji
EN
Abstrakty
EN
In this paper we study asymptotic properties of multidimensional Lasota equation. We give the conditions of its stability and chaos in the sense of Devaney in Orlicz spaces Lp for any p > 0. We also give criteria when the semigroup generated by the equation has not asymptotic behaviour.
Słowa kluczowe
Rocznik
Strony
387--397
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
  • Faculty of Mathematics and Computer Science, Jagiellonian University ul. Łojasiewicza 6, 30-348 Kraków, Poland
autor
  • Faculty of Computer Science, Bialystok University of Technology, ul. Wiejska 45A, 15-351 Białystok, Poland
Bibliografia
  • 1. BANASIAK, J. and LACHOWICZ, M. (2002) Topological chaos for birth-anddeath-type models with proliferation. Math. Models Methods Appl. Sci. 12, 755–775.
  • 2. BANKS, J., BROOKS, J., CAIRNS, G., DAVIS, G. and STACEY, P. (1992) On Devaney’s definition of chaos. Amer. Math. Monthly 99, 332–334.
  • 3. BIELACZYC, T. (2010) Generic properties of measures invariant with respekt to the Wa˙zewska partial differential equation. J. Math. Anal. Appl. 372, 1–7.
  • 4. BRZEŹNIAK, Z. and DAWIDOWICZ, A.L. (2009) On periodic solutions to the von Foerster-Lasota equation. Semigroup Forum 78 (1), 118–137.
  • 5. DAWIDOWICZ, A.L. and POSKROBKO, A. (2008) On chaotic and stable behaviour of the von Foerster-Lasota equation in some Orlicz spaces. Proc. Est. Acad. Sci. 57 (2), 61–69.
  • 6. DEVANEY, R.L. (1989) An Introduction to Chaotic Dynamical Systems. Addison–Wesley, New York.
  • 7. HARTMAN, P. (1964) Ordinary Differential Equations. John Wiley & Sons, New York.
  • 8. LASOTA, A. (1981) Stable and chaotic solutions of a first order partial differentia equation. Nonlinear Anal. 5 (11), 1181–1193.
  • 9. LASOTA, A., MACKEY, M. C. and WAŻEWSKA-CZYŻEWSKA, M. (1981) Minimizing Therapeutically Induced Anemia. J. Math. Biology 13, 149–158.
  • 10. LASOTA, A. and SZAREK, T. (2004) Dimension of measures invariant with respect to Ważewska partial differential equation. J. Differential Equations 196 (2), 448–465.
  • 11. LESZCZYŃSKI, H. (2008) Differential functional von Foerster equations with renewal. Condensed Matter Physics 54 (2), 361-370.
  • 12. LESZCZYŃSKI, H. and ZWIERKOWSKI, P. (2007) Iterative methods for generalized von Foerster equations with functional dependence. J. Inequal. Appl. Art. ID 12324, 14.
  • 13. ŁOSKOT, K. (1985) Turbulent solutions of first order partial differential equation. J. Differential Equations 58 (1), 1–14.
  • 14. ŁOSKOT, K. (1991) Stable solutions of a system of first order partial differentia equations. Bull. Polish Acad. Sci. Math. 39 (3-4), 151–159.
  • 15. MALIGRANDA, L. (1989) Orlicz spaces and interpolation. Universidade Estadual de Campinas, Departamento de Matemática, Campinas.
  • 16. MUSIELAK, J. (1983) Orlicz Spaces and Modular Spaces. Springer-Verlag, Berlin.
  • 17. RAMKRISHNA, D. (1979) Statistical models of cell populations. Advances in Biochemical Engineering 11, 1–47.
  • 18. RUDNICKI, R. (1985) Invariant measures for the flow of a first order partial differential equation. Ergod. Th. & Dynam. Systems 5 (3), 437–443.
  • 19. TESCHL, G. (2012) Ordinary Differential Equations and Dynamical Systems. American Mathematical Society, Providence.
  • 20. WAŻEWSKA-CZYŻEWSKA, M. and LASOTA, A. (1976)Matematyczne problemy dynamiki układu krwinek czerwonych. (Mathematical problems of dynamics of the red cell system; in Polish).Roczniki PTM, Mat. Stos. VI, 23–40.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-9580908b-0a1f-48ec-825e-b9dbaa2416e4
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