Pure multiplicative stochastic resonance of a theoretical anti-tumor model with seasonal modulability.

Pure multiplicative noise-induced stochastic resonance, which appears in an anti-tumor system modulated by a seasonal external field, is studied by using theoretical analyses of the generalized potential and numerical simulations. For optimally selected values of the multiplicative noise intensity stochastic resonance is observed, which is manifested by the quasisymmetry of two potential minima. Theoretical results and numerical simulations are in good quantitative agreement.

[1]  S. I. Nikitin,et al.  STOCHASTIC RESONANCE AT HIGHER HARMONICS IN MONOSTABLE SYSTEMS , 1997 .

[2]  A Romano,et al.  Analysis of a "phase transition" from tumor growth to latency. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  Ricard V Solé,et al.  An error catastrophe in cancer? , 2004, Journal of theoretical biology.

[4]  Jing-hui Li,et al.  Effect of asymmetry on stochastic resonance and stochastic resonance induced by multiplicative noise and by mean-field coupling. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  James D. Murray Mathematical Biology: I. An Introduction , 2007 .

[6]  Santucci,et al.  Multiplicative stochastic resonance. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  B. Ai,et al.  Correlated noise in a logistic growth model. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  A. Brú,et al.  The universal dynamics of tumor growth. , 2003, Biophysical journal.

[9]  I. Tannock,et al.  Repopulation of cancer cells during therapy: an important cause of treatment failure , 2005, Nature Reviews Cancer.

[10]  Vilar,et al.  Divergent Signal-to-Noise Ratio and Stochastic Resonance in Monostable Systems. , 1996, Physical review letters.

[11]  Helen Byrne,et al.  Asymmetric growth of models of avascular solid tumours: exploiting symmetries. , 2002, IMA journal of mathematics applied in medicine and biology.

[12]  Konstantina S. Nikita,et al.  In silico radiation oncology: combining novel simulation algorithms with current visualization techniques , 2002, Proc. IEEE.

[13]  C. S. Holling,et al.  Qualitative Analysis of Insect Outbreak Systems: The Spruce Budworm and Forest , 1978 .

[14]  B. Robinson,et al.  Immunotherapy and chemotherapy — a practical partnership , 2005, Nature Reviews Cancer.

[15]  D. Benbrook,et al.  Nature Reviews Cancer , 2003 .

[16]  Khachik Sargsyan,et al.  A numerical method for some stochastic differential equations with multiplicative noise , 2005 .

[17]  M. Bjornsti,et al.  Enhanced antitumor activity of irofulven in combination with irinotecan in pediatric solid tumor xenograft models , 2005, Cancer Chemotherapy and Pharmacology.

[18]  Ling Zhang,et al.  The stationary properties and the state transition of the tumor cell growth mode , 2004 .

[19]  Liu Liang-gang,et al.  Fluctuation of Parameters in Tumor Cell Growth Model , 2003 .

[20]  Wiesenfeld,et al.  Theory of stochastic resonance. , 1989, Physical review. A, General physics.

[21]  Frank Moss,et al.  Use of behavioural stochastic resonance by paddle fish for feeding , 1999, Nature.

[22]  Jia,et al.  Stochastic resonance in a bistable system subject to multiplicative and additive noise , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.