Effects of Noises in Some Complex Nonlinear and Biological Systems

• Chin-Kun Hu (胡進錕)Institute of Physics, Academia Sinica,Taipei 11529, Taiwan

• E-mail: huck@phys.sinica.edu.tw• http://proj1.sinica.edu.tw/~statphys/

At The 4th China-Europe Summer School on Complexity Science , Shanghai, 13 August 2010

Taiwan President

Shui-Bian Chen,

Democratic Progressive Party(20 May 2000-20 May 2008)

Taiwan President

Ying-Jeou Ma

National Party(KMT)(20 May 2008-20 May 2012)

President of Academia Sinica

Y.-T. Lee (January 1994-October 2006), Winner of Nobel Prize in Chemistry in 1986

President of Academia Sinica, Chi-Huey Wong (October 2006-October 2011)

Academia Sinica is directly under Taiwan President’s office.

N. Sh. Izmailian, V. B. Priezzhev, P. Ruelle, and C.-K. Hu, Phys. Rev. Lett. 95, 260602 (2005)

Critical behavior of the dimer model on square and triangular latticesN. Sh. Izmailian, K. B. Oganesyan, M.-C. Wu, and C.-K. Hu,

Phys. Rev. E 73, 016128 (2006).

C=-2 for all cases.

Yao-Cheng Hung (洪耀正) and Chin-Kun Hu (胡進錕) Chaotic communication via temporal transfer entropy,

Phys. Rev. Lett. 101, 244102(2008).

• How to evaluate causal relationship between two time series?

• Application: chaotic communications

M.-S. Li, C.-K. Hu, D. K. Klimov, and D. Thirumalai, Proc. Natl. Acad. Sci. USA 103, 93 (2006).

Fernandez and Li, Science 303, 1674(2004): AFM

Molecular models of biological (virus) evolution

Saakian and Hu, PNAS 103, 4935(2006) Phys. Rev. E. 73, 041913 (2006)

Diploid model.

Phys. Rev. E 77, 061907 (2008)

Phys. Rev. E 79, 031903(2009)

The 7th Dynamic Days Asia- Pacific (DDAP7)

At Academia Sinica, Taipei, TaiwanAugust 2012

The detail can be found in early 2011 athttp://proj1.sinica.edu.tw/~statphys.

Outline

• Various noises • Effects of noises on synchronization of

nonlinear systems• Effects of noises on p53 regulatory network• Effects of noises on protein folding rates• Final comments

Langevin Equation with Gaussian & non-Gaussian colored noises

What is Synchronization?

Influence of noise on the synchronization of the stochastic Kuramoto model, B. C. Bag, K. G. Petrosyan, and C.-K. Hu,

Phys. Rev. E 76, 056210 (2007).• We consider the Kuramoto model of globally

coupled phase oscillators subject to Ornstein- Uhlenbeck and non-Gaussian colored noise and investigate the influence of noise on the order parameter of the synchronization process. We use numerical methods to study the dependence of the threshold as well as the maximum degree of synchronization on the correlation time and the strength of the noise, and find that the threshold of synchronization strongly depends on the nature of the noise.

Y. Kuramoto, Prog. Theor. Phys. Suppl., 79, 223 (1984).

Stochastic Kuramoto model with time-delayed interactions

Constructive role of noise in p53 regulatory network

Yao-Chen Hung and Chin-Kun HuComputer Physics Communications,

in press (2010)

Effects of noises in protein folding rates

Bidhan Chandra Bag, Chin-Kun Hu, Mai Suan Li,

Phys. Chem. &Chem. Phys. (2010)

16 a.a. 36a.a.

76a.a.

For hairpin

For ubiquitin

Our papers on synchronization• P. M. Gade and C.-K. Hu. Synchronization and coherence in thermodynamic

coupled map lattices with intermediate-range coupling, Phys. Rev. E. 60, 4966(1999).

• P.M. Gade and C.-K. Hu. Synchronous chaos in coupled map lattices with small-world interactions, Phys. Rev. E 62, 6409 (2000).

• S. Jalan, R. E. Amritkar, and C.-K. Hu. Synchronized clusters in coupled map networks. I. Numerical studies, Phys. Rev. E 72, 016211 (2005).

• R. E. Amritkar, S. Jalan, and C.-K. Hu. Synchronized clusters in coupled map networks. II. Stability analysis, Phys. Rev. E 72, 016212 (2005).

• R. E. Amritkar and C.-K. Hu, Synchronized state of coupled dynamics on time-varying networks, Chaos 16, 015117 (2006).

• P. M. Gade and C.-K. Hu, Scaling and universality in transition to synchronous chaos with local-global interactions, Phys. Rev. E 73, 036212 (2006).

• M.-C. Wu and C.-K. Hu, Empirical mode decomposition and synchrogram approach to cardiorespiratory synchronization, Phys. Rev. E 73, 051917 (2006).

• B. C. Bag, K. G. Petrosyan, and C.-K. Hu, Influence of noises on the synchronization of the stochastic Kuramoto model, Phys. Rev. E 76, 056210 (2007).

• M. K. Sen, B. C. Bag, K. G. Petrosyan, and C.-K. Hu. Effect of time delay on the onset of synchronization of the stochastic Kuramoto model, J. Stat. Mech. Theory and Exp., P08018 (2010).

Our papers on effects of noises on complex biological systems

• Y. C. Hung and C.-K. Hu. Constructive role of noise in p53 regulatory network, Comp. Phys. Commu., in press (2010).

• B. C. Bag, C.-K. Hu, and M. S. Li, Colored Noise, Folding Rates and Departure from Kramers’ Behavior, Phys. Chem. Chem. Phys. in press (2010).

Final Comments

• Noises and a delay play important role in synchronization in nonlinear systems.

• Noises play a constructive role in p53 regulatory network.

• Noises effect the protein folding rate.

B. C. Bag and C.-K. Hu. Current inversion induced by colored non-Gaussian noise, J. Stat. Mech.:

Theory and Experiment, p02003 (2009).