Dynamics of birth-and-death processes with proliferation - Stability and chaos

Discrete and Continuous Dynamical Systems

Volumn 29, Issue 1, 2011, Pages 67-79

  Banasiak, Jacek ^a,b   Moszyński, Marcin ^c  

^a UNIVERSITY OF KWAZULU NATAL   (South Africa)

^b LODZ UNIVERSITY OF TECHNOLOGY   (Poland)

^c UNIVERSITY OF WARSAW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79551688613     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2011.29.67     Document Type: Article

References (18)

1. J. Banasiak, Chaotic linear systems in mathematical biology, South African Journal of Sci- ence, 104 (2008), 173-179.
2. J. Banasiak and M. Lachowicz, Chaos for a class of linear kinetic models, Compt. Rend. Acad. Sci. Paris, 329, Série IIb, (2001), 439-444. (Pubitemid 32734132)
3. nd International Conference, Rio de Janeiro, 2001, Optimization Software Inc., Publications, New York - Los Angeles, 2002, 32-44.
4. J. Banasiak and M. Lachowicz, Topological chaos for birth-and-death-type models with pro- liferation, Math. Models Methods Appl. Sci., 12 (2002), 755-775.
5. J. Banasiak, M. Lachowicz and M. Moszyński, Chaotic behavior of semigroups related to the process of gene amplification-deamplification with cells' proliferation, Math. Biosciences, 206 (2007), 200-215. (Pubitemid 46483525)
6. J. Banasiak and M. Moszyński, A generalization of Desch-Schappacher-Webb criteria for chaos, Discrete and Continuous Dynamical Systems - A, 12 (2005), 959-972. (Pubitemid 40622741)
7. J. Banasiak and M. Moszyński, Hypercyclicity and chaoticity spaces of C0-semigroups, Discr. Cont. Dyn. Sys.-A, 20 (2008), 577-587.
8. A. Bobrowski and M. Kimmel, Asymptotic behaviour of an operator exponential related to branching random walk models of DNA repeats, Journal of Biological Systems, 7 (1999), 33-43. (Pubitemid 129628923)
9. W. Desch, W. Schappacher and G. F. Webb, Hypercyclic and chaotic semigroups of linear operators, Ergodic Theory Dynam. Systems, 17 (1997), 793-819. (Pubitemid 127346957)
10. S. El Mourchid, The imaginary point spectrum and hypercyclicity, Semigroup Forum, 73 (2006), 313-316.
11. S. N. Elaydi, "An Introduction to Difference Equations," Springer Verlag, New York, 1999.
12. K.-J. Engel and R. Nagel, "One-parameter Semigroups for Linear Evolution Equations," Springer-Verlag, New York, 2000.
13. K.-J. Engel and R. Nagel, "A Short Course on Operator Semigroups," Springer Sci- ence+Business Media, New York, 2006.
14. W. Feller, "An Introduction to Probability and its Applications," vol. 1, 3rd edition, J. Wiley, New York, 1968.
15. M. Kimmel and D. N. Stivers, Time-continuous branching walk models of unstable gene amplification, Bull. Math. Biol., 50 (1994), 337-357.
16. M. Kimmel, A. Świerniak and A. Polański, Infinite-dimensional model of evolution of drug resistance of cancer cells, J. Math. Systems Estimation Control, 8 (1998), 1-16.
17. E. H. Spanier, "Algebraic Topology," McGraw-Hill, New York-Toronto, Ont.-London, 1966.
18. A. Świerniak, A. Polański and M. Kimmel, Control problems arising in chemotherapy under evolving drug resisitance, Preprints of the 13th World Congress of IFAC 1996, Volume B, 411-416.