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In this paper, the mean first-passage times for a cancer development system driven by colored cross-correlated noises are investigated. Based on the Novikov theorem and the Fox approach, the approximate Fokker-Planck equation and the explicit expressions of the mean first-passage time are derived. Numerical results show that: if the coupling strength between the two noises is negative, the mean first-passage time is a decreasing function of the two noise intensities, but an increasing function of the correlation time; if the coupling strength between the two noises is positive, then the value of the monotonic mean first-passage time versus the additive noise intensity depends on the transition direction. And in addition, the mean first-passage time is a non-monotonic function of the multiplicative noise intensity, but a decreasing function of the correlation time.
[1] ［1］Gammaitoni L, Hnggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[2] ［2］Wellens T, Shatokhin V, Buchleitner A 2004 Rep. Prog. Phys. 67 45
[3] ［3］Lindner B, García-Ojalvo, Neiman A, Schimansky-Geier L 2004 Phys. Rep. 392 321
[4] ［4］Wu D, Zhu S Q 2007 Phys. Lett. A 363 202
[5] ［5］Luo X Q, Zhu S Q 2003 Phys. Rev. E 67 021104
[6] ［6］Zhang X Y, Xu W 2007 Physica A 385 95
[7] ［7］Zhou B C, Xu W 2008 Chaos Solitons Fract. 38 1146
[8] ［8］Madureira A J R, Hnggi P, Wio H S 1996 Phys. Lett. A 217 248
[9] ［9］Wang C J, Wei Q, Zheng B B, Mei D C 2008 Acta Phys. Sin. 57 1375 (in Chinese) ［王参军、魏群、郑宝兵、梅冬成 2008 57 1375］
[10] ］Wang C J, Mei D C 2008 Acta Phys. Sin. 57 3983 (in Chinese) ［王参军、梅冬成 2008 57 3983］
[11] ］Jin Y F, Xu W, Ma S J, Li W 2005 Acta Phys. Sin. 54 3480 (in Chinese) ［靳艳飞、徐伟、马少娟、李伟 2005 54 3480］
[12] ］Ochab-Marcinek A, Gudowska-Nowak E 2004 Physica A 343 557
[13] ］Fiasconaro A, Spagnolo B 2006 Phys. Rev. E 74 041904
[14] ］Novikov E A, ksp Z 1965 Sov. Phys. JEPT 20 1290
[15] ］Fox R F 1986 Phys. Rev. A 34 4525
[16] ］Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Scientific and Technological Education Publishing House) p134 (in Chinese) ［胡岗 1994 随机力与非线性系统 (上海：上海科技教育出版社) 第134页］
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[1] ［1］Gammaitoni L, Hnggi P, Jung P, Marchesoni F 1998 Rev. Mod. Phys. 70 223
[2] ［2］Wellens T, Shatokhin V, Buchleitner A 2004 Rep. Prog. Phys. 67 45
[3] ［3］Lindner B, García-Ojalvo, Neiman A, Schimansky-Geier L 2004 Phys. Rep. 392 321
[4] ［4］Wu D, Zhu S Q 2007 Phys. Lett. A 363 202
[5] ［5］Luo X Q, Zhu S Q 2003 Phys. Rev. E 67 021104
[6] ［6］Zhang X Y, Xu W 2007 Physica A 385 95
[7] ［7］Zhou B C, Xu W 2008 Chaos Solitons Fract. 38 1146
[8] ［8］Madureira A J R, Hnggi P, Wio H S 1996 Phys. Lett. A 217 248
[9] ［9］Wang C J, Wei Q, Zheng B B, Mei D C 2008 Acta Phys. Sin. 57 1375 (in Chinese) ［王参军、魏群、郑宝兵、梅冬成 2008 57 1375］
[10] ］Wang C J, Mei D C 2008 Acta Phys. Sin. 57 3983 (in Chinese) ［王参军、梅冬成 2008 57 3983］
[11] ］Jin Y F, Xu W, Ma S J, Li W 2005 Acta Phys. Sin. 54 3480 (in Chinese) ［靳艳飞、徐伟、马少娟、李伟 2005 54 3480］
[12] ］Ochab-Marcinek A, Gudowska-Nowak E 2004 Physica A 343 557
[13] ］Fiasconaro A, Spagnolo B 2006 Phys. Rev. E 74 041904
[14] ］Novikov E A, ksp Z 1965 Sov. Phys. JEPT 20 1290
[15] ］Fox R F 1986 Phys. Rev. A 34 4525
[16] ］Hu G 1994 Stochastic Forces and Nonlinear Systems (Shanghai: Shanghai Scientific and Technological Education Publishing House) p134 (in Chinese) ［胡岗 1994 随机力与非线性系统 (上海：上海科技教育出版社) 第134页］
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