Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access February 26, 2011

Stochastic tumor growth system with two different kinds of time delay

Chun-Sheng Dou, Di Li and Can-Jun Wang
From the journal Open Physics

Abstract

The dynamical properties of a noise-driven tumor cell growth system are investigated when there exist two different kinds of time delays, in the deterministic and fluctuating forces, respectively. Using the approximation probability density approach, the delayed Fokker-Planck equation is obtained. The effects of two different time delays on the stationary probability distribution (SPD), the mean value and the mean passage time (MFPT) are discussed. It is found that the time delay τ1 in the deterministic force can enhance tumor cell number, while the time delay τ2 in the fluctuating force can induce a decrease in tumor cell numbers. On the other hand, while τ1 can hold back the extinction of tumor cells, τ2 can speed up their extinction.

[1] A. Longtin, A. Bulsara, F. Moss, Phys. Rev. Lett. 67, 656 (1991) http://dx.doi.org/10.1103/PhysRevLett.67.65610.1103/PhysRevLett.67.656Search in Google Scholar PubMed

[2] J.J. Collins, T.T. Imhoff, P. Grigg, Phys. Rev. E 56, 923 (1997) http://dx.doi.org/10.1103/PhysRevE.56.92310.1103/PhysRevE.56.923Search in Google Scholar

[3] C. Masoller, Phys. Rev. Lett. 88, 034102 (2002) http://dx.doi.org/10.1103/PhysRevLett.88.03410210.1103/PhysRevLett.88.034102Search in Google Scholar PubMed

[4] D. Huber, L.S. Tsimring, Phys. Rev. Lett. 91, 260601 (2003) http://dx.doi.org/10.1103/PhysRevLett.91.26060110.1103/PhysRevLett.91.260601Search in Google Scholar PubMed

[5] L.S. Tsimring, A. Pikovsky, Phys. Rev. Lett. 87, 250602 (2001) http://dx.doi.org/10.1103/PhysRevLett.87.25060210.1103/PhysRevLett.87.250602Search in Google Scholar PubMed

[6] D. Wu, S.Q. Zhu, Phys. Lett. A 363, 202 (2007) http://dx.doi.org/10.1016/j.physleta.2006.11.00610.1016/j.physleta.2006.11.006Search in Google Scholar

[7] L.R. Nie, D.C. Mei, Europhys. Lett. 79, 20005 (2007) http://dx.doi.org/10.1209/0295-5075/79/2000510.1209/0295-5075/79/20005Search in Google Scholar

[8] L.R. Nie, D.C. Mei, Phys. Rev. E 77, 031107 (2008) http://dx.doi.org/10.1103/PhysRevE.77.03110710.1103/PhysRevE.77.031107Search in Google Scholar PubMed

[9] D. Bratsun, D. Volfson, L.S. Tsimring, J. Hasty, PANS 41, 14593 (2005) http://dx.doi.org/10.1073/pnas.050385810210.1073/pnas.0503858102Search in Google Scholar PubMed PubMed Central

[10] B.Q. Ai, X.J. Wang, G.T. Liu, L.G. Liu, Phys. Rev. E 67, 022903 (2003) http://dx.doi.org/10.1103/PhysRevE.67.02290310.1103/PhysRevE.67.022903Search in Google Scholar PubMed

[11] D.C. Mei, C.W. Xie, L. Zhang, Eur. Phys. J. B 41, 107 (2004) http://dx.doi.org/10.1140/epjb/e2004-00300-110.1140/epjb/e2004-00300-1Search in Google Scholar

[12] J.C. Cai, C.J. Wang, D.C. Mei, Chinese Phys. Lett. 24, 1162 (2007) http://dx.doi.org/10.1088/0256-307X/24/5/01010.1088/0256-307X/24/5/010Search in Google Scholar

[13] C.J. Wang, Q. Wei, D.C. Mei, Mod. Phys. Lett. B 21, 789 (2007) http://dx.doi.org/10.1142/S021798490701322510.1142/S0217984907013225Search in Google Scholar

[14] C.J. Wang, Q. Wei, D.C. Mei, Phys. Lett. A 372, 2176 (2008) http://dx.doi.org/10.1016/j.physleta.2007.11.04010.1016/j.physleta.2007.11.040Search in Google Scholar

[15] C.J. Wang, Q. Wei, B.B. Zheng, D.C. Mei, Acta Phys. Sin.-Ch. Ed. 57, 1735 (2008) Search in Google Scholar

[16] L.B. Han, X.L. Gong, L. Cao, D.J. Wu, Chinese Phys. Lett. 24, 632 (2007) http://dx.doi.org/10.1088/0256-307X/24/4/02410.1088/0256-307X/24/4/024Search in Google Scholar

[17] W.R. Zhong, Y.Z. Shao, Z.H. He, Phys. Rev. E 73, 060902 (2006) http://dx.doi.org/10.1103/PhysRevE.73.06090210.1103/PhysRevE.73.060902Search in Google Scholar

[18] T. Bose, S. Trimper, Phys. Rev. E 79, 051903 (2009) http://dx.doi.org/10.1103/PhysRevE.79.05190310.1103/PhysRevE.79.051903Search in Google Scholar

[19] L.B. Han, Acta Phys. Sin.-Ch. Ed. 57, 6081 (2008) 10.7498/aps.57.6081Search in Google Scholar

[20] Y.F. Guo, W. Xu, Acta Phys. Sin.-Ch. Ed. 57, 2699 (2008) 10.7498/aps.57.2699Search in Google Scholar

[21] A. Lipowski, D. Lipowska, Physica A 276, 456 (2000) http://dx.doi.org/10.1016/S0378-4371(99)00482-310.1016/S0378-4371(99)00482-3Search in Google Scholar

[22] J.C. Panetta, Appl. Math. Lett. 8, 83 (1995) http://dx.doi.org/10.1016/0893-9659(95)00053-S10.1016/0893-9659(95)00053-SSearch in Google Scholar

[23] X.H. Gu, S.Q. Zhu, D. Wu, Eur. Phys. J. D 42, 461 (2007) http://dx.doi.org/10.1140/epjd/e2007-00043-710.1140/epjd/e2007-00043-7Search in Google Scholar

[24] T.D. Frank, P.J. Beek, Phys. Rev. E 64, 021917 (2001) http://dx.doi.org/10.1103/PhysRevE.64.02191710.1103/PhysRevE.64.021917Search in Google Scholar PubMed

[25] D.J. Wu, L. Cao, S.Z. Ke, Phys. Rev. E 50, 2496 (1994) http://dx.doi.org/10.1103/PhysRevE.50.356010.1103/PhysRevE.50.3560Search in Google Scholar

[26] K. Lindenberg, B.J. West, J. Stat. Phys. 42, 201 (1986) http://dx.doi.org/10.1007/BF0101084710.1007/BF01010847Search in Google Scholar

[27] J. Masoliver, B.J. West, K. Lindenberg, Phys. Rev. A 35, 3086 (1987) http://dx.doi.org/10.1103/PhysRevA.35.308610.1103/PhysRevA.35.3086Search in Google Scholar PubMed

Published Online: 2011-2-26
Published in Print: 2011-6-1

© 2010 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Scroll Up Arrow