Delay-induced state transition and resonance in periodically driven tumor model with immune surveillance

• Autorzy: Tao Yang , Qinglin Han , Chunhua Zeng , Hua Wang , Yunchang Fu , Chun Zhang
• Języki publikacji: EN

Abstrakty

EN

The phenomenon of stochastic resonance (SR) in a tumor growth model under the presence of immune surveillance is investigated. Time delay and cross-correlation between multiplicative and additive noises are considered in the system. The signal-to-noise ratio (SNR) is calculated when periodic signal is introduced multiplicatively. Our results show that: (i) the time delay can accelerate the transition from the state of stable tumor to that of extinction, however the correlation between two noises can accelerate the transition from the state of extinction to that of stable tumor; (ii) the time delay and correlation between two noises can lead to a transition between SR and double SR in the curve of SNR as a function of additive noise intensity, however for the curve of SNR as a function of multiplicative noise intensity, the time delay can cause the SR phenomenon to disappear, and the cross-correlation between two noises can lead to a transition from SR to stochastic reverse-resonance. Finally, we compare the SR phenomenon for the multiplicative periodic signal with that for additive periodic signal in the tumor growth model with immune surveillance.

Słowa kluczowe

EN

noise; time delay; tumor growth model; stochastic resonance

• Czasopismo: Open Physics
• Rocznik: 2014
• Tom: 12
• Numer: 6
• Strony: 383-391

Daty

wydano

2014-06-01

online

2014-05-31

Twórcy

autor

Tao Yang

• Faculty of Science, Kunming University of Science and Technology, Kunming, 650093, Yunnan, China

autor

Qinglin Han

• Faculty of Science, Kunming University of Science and Technology, Kunming, 650093, Yunnan, China

autor

Chunhua Zeng,

autor

Hua Wang

• State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Kunming, 650093, China

autor

Yunchang Fu

• Faculty of Science, Kunming University of Science and Technology, Kunming, 650093, Yunnan, China

autor

Chun Zhang

• Faculty of Science, Kunming University of Science and Technology, Kunming, 650093, Yunnan, China

Bibliografia

• [1] R. Benzi, A. Sutera, A. Vulpiani J. Phys. A: Math. Gen. 14, L453 (1981) http://dx.doi.org/10.1088/0305-4470/14/11/006[Crossref]
• [2] R. Benzi, G. Parisi, A. Sutera, A. Vulpiani, Tellus 34, 10 (1982) http://dx.doi.org/10.1111/j.2153-3490.1982.tb01787.x[Crossref]
• [3] C. Nicolis, G. Nicolis, Tellus 33, 225 (1981) http://dx.doi.org/10.1111/j.2153-3490.1981.tb01746.x[Crossref]
• [4] C. Nicolis, Tellus 34, 1 (1982) http://dx.doi.org/10.1111/j.2153-3490.1982.tb01786.x[Crossref]
• [5] L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni Rev. Mod. Phys. 70, 223 (1998) http://dx.doi.org/10.1103/RevModPhys.70.223[Crossref]
• [6] R. N. Mantegna, B. Spagnolo, Nuovo Cimento D 17, 873 (1995) http://dx.doi.org/10.1007/BF02451845[Crossref]
• [7] E. Lanzara, R.N. Mantegna, B. Spagnolo, R. Zangara, Am. J. Phys. 65, 341 (1997) http://dx.doi.org/10.1119/1.18520[Crossref]
• [8] W. R. Zhong, Y. Z. Shao, Z. H. He, Phys. Rev. E 73, 060902 (2006) http://dx.doi.org/10.1103/PhysRevE.73.060902[Crossref]
• [9] C. H. Zeng, C. W. Xie, Mod. Phys. Lett. B 13, 1651 (2009) http://dx.doi.org/10.1142/S021798490901982X[Crossref]
• [10] A. Joshi, M. Xiao, Phys. Rev. A 74, 013817 (2006) http://dx.doi.org/10.1103/PhysRevA.74.013817[Crossref]
• [11] Y. Jia, S. N. Yu, J. R. Li, Phys. Rev. E 62, 1869 (2000) http://dx.doi.org/10.1103/PhysRevE.62.1869[Crossref]
• [12] Y. Jia, X. P. Zheng, X. M. Hu, J. H. Li, Phys. Rev. E 63, 031107 (2001) http://dx.doi.org/10.1103/PhysRevE.63.031107[Crossref]
• [13] X. Q. Luo, S. Q. Zhu, Phys. Rev. E 67, 021104 (2003) http://dx.doi.org/10.1103/PhysRevE.67.021104[Crossref]
• [14] D. J. Wu, S. Q. Zhu, Phys. Lett. A 363, 202 (2007) http://dx.doi.org/10.1016/j.physleta.2006.11.006[Crossref]
• [15] A. Fiasconaro, B. Spagnolo, A. Ochab-Marcinek, E. Gudowska-Nowak Phys. Rev. E 74, 041904 (2006) http://dx.doi.org/10.1103/PhysRevE.74.041904[Crossref]
• [16] W. R. Zhong, Y. Z. Shao, Z. H. He, Phys. Rev. E 74, 011916 (2006) http://dx.doi.org/10.1103/PhysRevE.74.011916[Crossref]
• [17] W. R. Zhong, Y. Z. Shao, L. Li, F. H Wang, Z. H. He, Europhys. Lett. 82, 20003 (2008) http://dx.doi.org/10.1209/0295-5075/82/20003[Crossref]
• [18] T. Bose, S. Trimper, Phys. Rev. E 79, 051903 (2009) http://dx.doi.org/10.1103/PhysRevE.79.051903[Crossref]
• [19] B. Spagnolo, A. La Barbera, Physica A 315, 114 (2002) http://dx.doi.org/10.1016/S0378-4371(02)01245-1[Crossref]
• [20] D. Valenti, A. Fiasconaro, B. Spagnolo, Physica A, 331, 477 (2004) http://dx.doi.org/10.1016/j.physa.2003.09.036[Crossref]
• [21] C. H. Zeng, H. Wang, J. Stat. Phys. 141, 889 (2010) http://dx.doi.org/10.1007/s10955-010-0068-8[Crossref]
• [22] J. Yu, G. Hu, B. K. Ma, Phys. Rev. B 39, 4572 (1989) http://dx.doi.org/10.1103/PhysRevB.39.4572[Crossref]
• [23] M. Molski, J. Konarski, Phys. Rev. E 68, 021916 (2003) http://dx.doi.org/10.1103/PhysRevE.68.021916[Crossref]
• [24] 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.67.022903[Crossref]
• [25] A. Behera, S. F. O Rourke, Phys. Rev. E 77, 013901 (2008) http://dx.doi.org/10.1103/PhysRevE.77.013901[Crossref]
• [26] B. Q. Ai, X. J. Wang, L. G. Liu, Phys. Rev. E 77, 013902 (2008) http://dx.doi.org/10.1103/PhysRevE.77.013902[Crossref]
• [27] D. C. Mei, C. W. Xie, L. Zhang, Eur. Phys. J. B 41, 107 (2004) http://dx.doi.org/10.1140/epjb/e2004-00300-1[Crossref]
• [28] C. J. Wang, Q. Wei, D. C. Mei, Mod. Phys. Lett. B 21, 789 (2007) http://dx.doi.org/10.1142/S0217984907013225[Crossref]
• [29] C. J. Wang, Q. Wei, D. C. Mei, Phys. Lett. A 372, 2176 (2008) http://dx.doi.org/10.1016/j.physleta.2007.11.040[Crossref]
• [30] G. P. Dunn, L. J. Old, R. D. Schreiber, Annu. Rev. Immunol. 22, 329 (2004) http://dx.doi.org/10.1146/annurev.immunol.22.012703.104803[Crossref]
• [31] R. Kim, M. Emi, K. Tanabe, Immunol. 121, 1 (2007) http://dx.doi.org/10.1111/j.1365-2567.2007.02587.x[Crossref]
• [32] A. Fiasconaro, A. Ochab-Marcinek, B. Spagnolo, E. Gudowska-Nowak, Eur. Phys. J. B 65, 435 (2008) http://dx.doi.org/10.1140/epjb/e2008-00246-2[Crossref]
• [33] C. H. Zeng, X. F. Zhou, S. F. Tao, J. Phys. A: Math. Theor. 42, 495002 (2009) http://dx.doi.org/10.1088/1751-8113/42/49/495002[Crossref]
• [34] C. H. Zeng, Phys. Scr. 81, 025009 (2010) http://dx.doi.org/10.1088/0031-8949/81/02/025009[Crossref]
• [35] L. S. Tsimring, A. Pikovsky, Phys. Rev. Lett. 87, 250602 (2001) http://dx.doi.org/10.1103/PhysRevLett.87.250602[Crossref]
• [36] C. Masoller, Phys. Rev. Lett. 90, 020601 (2003) http://dx.doi.org/10.1103/PhysRevLett.90.020601[Crossref]
• [37] J. C. Cai, D. C. Mei, Mod. Phys. Lett. B 22, 2759 (2008) http://dx.doi.org/10.1142/S0217984908017291[Crossref]
• [38] D. Huber, L. S. Tsimring, Phys. Rev. Lett. 91, 260601 (2003) http://dx.doi.org/10.1103/PhysRevLett.91.260601[Crossref]
• [39] D. Curtin et al., Phys. Rev. E 70, 031103 (2004) http://dx.doi.org/10.1103/PhysRevE.70.031103[Crossref]
• [40] J. Houlihan, D. Goulding, Th. Busch, C. Masoller, G. Huyet, Phys. Rev. Lett. 92, 050601 (2004) http://dx.doi.org/10.1103/PhysRevLett.92.050601[Crossref]
• [41] M. C. Mackey, L. Glass, Science 197, 287 (1977) http://dx.doi.org/10.1126/science.267326[Crossref]
• [42] P. C. Bressoff, S. Coombes, Phys. Rev. Lett. 78, 4665 (1997) http://dx.doi.org/10.1103/PhysRevLett.78.4665[Crossref]
• [43] J. Garc a-Ojalvo, R. Roy, Phys. Lett. A 224, 51 (1996) http://dx.doi.org/10.1016/S0375-9601(96)00802-X[Crossref]
• [44] C. Masoller, Phys. Rev. Lett. 86, 2782 (2001) http://dx.doi.org/10.1103/PhysRevLett.86.2782[Crossref]
• [45] L. S. Tsimring, A. Pikovsky, Phys. Rev. Lett. 87, 250602 (2001) http://dx.doi.org/10.1103/PhysRevLett.87.250602[Crossref]
• [46] X. J. Tian, X. P. Zhang, F. Liu, W. Wang, Phys. Rev. E 80, 011926 (2009) http://dx.doi.org/10.1103/PhysRevE.80.011926[Crossref]
• [47] L. C. Du, D. C. Mei, Phys. Lett. A 374, 3275 (2010) http://dx.doi.org/10.1016/j.physleta.2010.06.003[Crossref]
• [48] C. H. Zeng, H. Wang, Chem. Phys. 402, 1 (2012) http://dx.doi.org/10.1016/j.chemphys.2012.02.020[Crossref]
• [49] W. Guo, L. C. Du, D. C. Mei, Phys. A 391, 1270 (2012) http://dx.doi.org/10.1016/j.physa.2011.11.007[Crossref]
• [50] R. Lefever, R. Garay, In: A. J. Valleron, P. D. M. Macdonald (Eds.), Local Description of Immune Tumor Rejection, Biomathematics and Cell Kinetics (Elsevier, North-Holland, Amsterdam, 1978) p. 333
• [51] J. J. Kim, I. F. Tannock, Nat. Rev. Cancer 5, 516 (2005) http://dx.doi.org/10.1038/nrc1650[Crossref]
• [52] X. Gu, S. Zhu, D. Wu, Eur. Phys. J. D 42, 461 (2007) http://dx.doi.org/10.1140/epjd/e2007-00043-7[Crossref]
• [53] D. J. Wu, L. Cao, S. Z. Ke, Phys. Rev. E 50, 2496 (1994) http://dx.doi.org/10.1103/PhysRevE.50.3560[Crossref]
• [54] S. Guillouzic, I. L’Heureux, A. Longtin, Phys. Rev. E 59, 3970 (1999) http://dx.doi.org/10.1103/PhysRevE.59.3970[Crossref]
• [55] S. Guillouzic, I. L’Heureux, A. Longtin, Phys. Rev. E 61, 4906 (2000) http://dx.doi.org/10.1103/PhysRevE.61.4906[Crossref]
• [56] T. D. Frank, Phys. Rev. E 72, 011112 (2005) http://dx.doi.org/10.1103/PhysRevE.72.011112[Crossref]
• [57] H. S. Wio, R. R. Deza, Eur. Phys. J. Spec. Top. 146, 111 (2007) http://dx.doi.org/10.1140/epjst/e2007-00173-0[Crossref]
• [58] H. Risken, The Fokker-Planck Equation: Methods of Solution and Applications (Springer, Berlin, 1992)
• [59] W. Horsthemke, R. Lefever, Noise-Induced Transitions (Springer, Berlin, 1984)
• [60] C. Van den Broeck, J. M. R. Parrondo, R. Toral, Phys. Rev. Lett. 73, 3395 (1994) http://dx.doi.org/10.1103/PhysRevLett.73.3395[Crossref]
• [61] J. Garcia-Ojalvo, J. M. Sancho, Noise in Spatially Extended Systems (Springer, Berlin, 1999) http://dx.doi.org/10.1007/978-1-4612-1536-3[Crossref]
• [62] P. Hänggi, F. Marchesoni, P. Z. Grigolini, Phys. B 56, 333 (1984)
• [63] R. F. Fox, Phys. Rev. A 33, 467 (1986) http://dx.doi.org/10.1103/PhysRevA.33.467[Crossref]
• [64] S. Bouzat, H. S. Wio, Phys. Rev. E 59, 5142 (1999) http://dx.doi.org/10.1103/PhysRevE.59.5142[Crossref]
• [65] H. S. Wio, S. Bouzat, Braz. J. Phys. 29, 136 (1999) http://dx.doi.org/10.1590/S0103-97331999000100012[Crossref]
• [66] P. S. Burada, G. Schmid, D. Reguera, J. M. Rubi, P. Hänggi, Europhys. Lett. 87, 50003 (2009) http://dx.doi.org/10.1209/0295-5075/87/50003[Crossref]

Identyfikatory

DOI

10.2478/s11534-014-0460-0