Abstract
Diverse complex dynamical systems are known to exhibit abrupt regime shifts at bifurcation points of the saddle-node type. The dynamics of most of these systems, however, have a stochastic component resulting in noise-driven regime shifts even if the system is away from the bifurcation points. In this paper, we propose a new quantitative measure, namely, the propensity transition point as an indicator of stochastic regime shifts. The concepts and the methodology are illustrated for the one-variable May model, a well-known model in ecology and the genetic toggle, a two-variable model of a simple genetic circuit. The general applicability and usefulness of the method for the analysis of regime shifts is further demonstrated in the case of the mycobacterial switch to persistence for which experimental data are available.
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References
H. Strogatz, Nonlinear Dynamics and Chaos - with Applications to Physics, Biology, Chemistry and Engineering (Addison-Wesley, 1994).
M. Scheffer et al., Nature 461, 53 (2009).
M. Scheffer, Critical Transitions in Nature and Society (Princeton University Press, 2009).
M. Scheffer, S.R. Carpenter, Trends Ecol. Evol. 18, 648 (2003).
T.M. Lenton, Nature Climate Change 1, 201 (2011).
J.G. Venegas et al., Nature 434, 777 (2005).
P.E. McSharry, L.A. Smith, L. Tarassenko, Nature Med. 9, 241 (2003).
E.M. Ozbudak, M. Thattai, H.N. Lim, B.I. Shraiman, A. Van Oudenaarden, Nature 427, 737 (2004).
J.R. Pomerening, Curr. Opin. Biotechnol. 19, 381 (2008).
J.E. Ferrell, W. Xiong, Chaos 11, 227 (2001).
L. Chen, R. Liu, Z.-P. Liu, M. Li, K. Aihara, Sci. Rep. 2, 342 (2012).
R.M. May, Nature 269, 471 (1977).
V. Guttal, C. Jayprakash, Ecol. Modell. 201, 420 (2007).
E. van Nes, M. Scheffer, M. Van der Bers, H. Coops, Aquatic Botany 72, 275 (2002).
V. Guttal, C. Jayaprakash, Ecol. Lett. 11, 450 (2008).
V. Dakos, E.H. Van Nes, P. D’Odorico, M. Scheffer, Ecology 93, 264 (2012).
M. Scheffer et al., Science 338, 344 (2012).
V. Horsthemke, R. Lefevre, Noise Induced Transitions (Springer-Verlag, Berlin, 1984).
T.B. Kepler, T.C. Elston, Biophys. J. 81, 3116 (2001).
C. Song et al., PLoS Comput. Biol. 6, e1000699 (2010).
A. Zakharova, T. Vadivasova, V. Anishchenko, A. Koseska, J. Kurths, Phys. Rev. E 81, 011106 (2010).
R. Karmakar, I. Bose, Phys. Biol. 4, 29 (2007).
M. Samoilov, S. Plyasunov, A.P. Arkin, Proc. Natl. Acad. Sci. U.S.A. 102, 2310 (2005).
T.L. To, N. Maheshri, Science 327, 1142 (2010).
T.S. Gardner, C.R. Cantor, J.J. Collins, Nature 403, 339 (2000).
D.T. Gillespie, J. Chem. Phys. 81, 2340 (1977).
K. Sureka, B. Ghosh, A. Dasgupta, J. Basu, M. Kundu, I. Bose, Plos One 3, e1771 (2008).
S. Ghosh, K. Sureka, B. Ghosh, I. Bose, J. Basu, M. Kundu, BMC Syst. Biol. 5, 18 (2011).
C.W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, Berlin, 1983).
N.G. van Kampen, Stochastic Processes in Physics and Chemistry (North Holland, Amsterdam, 1992).
H. Risken, The Fokker-Planck Equation (Springer-Verlag, Berlin, 1984).
W.D. Jin, C. Li, K.S. Zhi, Phys. Rev. E 50, 2496 (1994).
M. Rao, Y. Chen, B.C. Vemuri, Fei Wang, Inf. Theory, IEEE Trans. 50, 1220 (2004).
X.-D. Zheng, X.-Q. Yan, Y. Tau, PLoS One 6, e17104 (2011).
D.T. Gillespie, Markov Processes: An Introduction for Physical Scientists (Academic Press, London, 1992).
M. Scott, Tutorial: Genetic Circuits and Noise, 2006, available at M. Scott’s website.
R. Erban, J. Chapman, P. Maini (2007) arXiv:0704.1908[q-bio.SC].
D.T. Gillespie, A. Hellander, L.R. Petzold, J. Chem. Phys. 138, 170901 (2013).
D.T. Gillespie, Annu. Rev. Phys. Chem. 58, 35 (2007).
D.T. Gillespie, J. Chem. Phys. 113, 297 (2000).
W.K. Smits, O.P. Kuipers, J.-W. Veening, Nat. Rev. Microbiol. 4, 259 (2006).
H. Maamar, A. Raj, D. Dubnau, Science 317, 526 (2007).
A. Tiwari, G. Bálazsi, M.L. Gennaro, O.A. Igoshin, Phys. Biol. 7, 036005 (2010).
K. Sureka, B. Ghosh, A. Dasgupta, J. Basu, M. Kundu, I. Bose, unpublished data.
C. Wissel, Oecologia 65, 101 (1984).
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Ghosh, S., Pal, A.K. & Bose, I. Noise-induced regime shifts: A quantitative characterization. Eur. Phys. J. E 36, 123 (2013). https://doi.org/10.1140/epje/i2013-13123-y
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DOI: https://doi.org/10.1140/epje/i2013-13123-y