Influence of correlated noises on growth of a tumor in a modified verhulst model

Fluctuation and Noise Letters

Volumn 6, Issue 4, 2006, Pages

  Zhong, Wei Rong ^a   Shao, Yuan Zhi ^a   He, Zhen Hui ^a  

^a SUN YAT SEN UNIVERSITY   (China)

Author keywords

Correlation noise; Logistic model; Phase transition; Stochastic resonance; Tumor growth

Indexed keywords

EID: 33846099534     PISSN: 02194775     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219477506003495     Document Type: Article

References (27)

1. G. Nicolis and I. Prigogine, Self-organization in Nonequilibrium Systems (Wiley, New-York, 1977).
2. H. Haken, Advanced Synergetics (Springer Berlin, Heidelberg, 1985).
3. G. Nicolis and I. Prigogine, Exploring Complex (Freeman, New-York, 1986).
4. L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni, Rev. Mod Phys. 70 (1998) 223.
5. V. S. Anishchenko, V. V. Astakhov, A. B. Neiman, T. E. Vadivasova, and L. Schimansky-Geier, Nonlinear Dynamics of Chaotic and Stochastic Systems (Springer-Verlag Berlin, Heidelberg, 2002).
6. C. W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Science (Springer-Verlag, Berlin, 1983).
7. G. Hu, Stochastic Forces and Nonlinear Systems (Shanghai Scientific and Technological Education Publishing House, Shanghai, P. R. China, 1994) (in Chinese).
8. Y. Jia and J. R. Li, Phys. Rev. Lett. 78 (1997) 994.
9. Y. Jia and J. R. Li, Phys. Rev. E 53 (1996) 5786.
10. P. Hanggi and P. Riseborough, Phys. Rev. A 27 (1983) R3379.
11. B. McNamara, K. Weisenfeld and R. Roy, Phys. Rev. Lett. 60 (1988) 2626.
12. G. Hu, G. Nicolis, and C. Nicolis, Phys. Rev. A 42 (1990) 2030.
13. P. Jung and P. Hanggi, Phys. Rev. A 44 (1991) 8032.
14. M. I. Dykman, R. Mannella, P. V. E. McClintock, and N. G. Stocks, Phys. Rev. Lett. 68 (1992) 2985.
15. A. A. Zaikin, J. Kurths, and L. Schimansky-Geier, Phys. Rev. Lett. 85 (2000) 227.
16. M. Scalerandi and B. C. Sansone, Phys. Rev. Lett. 89 (2000) 218101.
17. P.-F. Verhulst. Recherche mathėmathiques sur le loi d'accroissement de la population. Nouveau Memoirės de l'Acadėmie Royale des Sciences et Belles Lettres de Bruxelles 18 (1845) 3-38.
18. R. B. Banks, Growth and Diffusion Phenomena (Springer-Verlag, Berlin Heidelberg, 1994).
19. J. D. Murray, Mathematical Biology I: An Introduction (Springer-Verlag, Berlin, Heidelberg, 2002).
20. A. Bru, J. M. Pastor, I. Fernaud, I. Bru, S. Melle, and C. Berenguer, Phys. Rev. Lett. 81 (1998) 4008.
21. A. Bru, S. Albertos, J. A. Lopez. Garcia-Asenjo, and I. Bru, Phys. Rev. Lett. 92 (2004) 238101.
22. A. Bru, S. Albertos, J. L. Subiza, J. L. Garcia-Asenjo, and I. Bru, Biophys. J. 85 (2003) 2948.
23. S. C. Ferreira, Jr, M. L. Martins, and M. J. Vilela, Phys. Rev. E 67 (2003) 051914.
24. B. Q. Ai, X. J. Wang, G. T. Liu, and L. G. Liu, Phys. Rev. E 67 (2003) 022903.
25. D. C. Mei, C. W. Xie, and L. Zhang, Eur. Phys. J. B 41 (2004) 107-112.
26. R. V. Sole and T. S. Deisboeck, J. Theor. Biol. 228 (2004) 47.
27. W. D. Jin, C. Li, and K. S. Zhi, Phys. Rev. E 50 (1994) 2496.