Abstract
We apply a nonlinear Markov chain model to examine decision making in the US house of representatives during the period between the bailout votes of September 29 and October 3, 2008. We show how to determine deterministic and stochastic properties of the nonlinear model and, in doing so, estimate the strength of the attractors and the amplitudes of fluctuating forces that putatively influenced representatives’ decision making.
Similar content being viewed by others
References
M. Takatsuji, Biol. Cybern. 17, 207 (1975)
B. Latane, A. Nowak, Behavioral science 39, 1 (1994)
S. Galam, J.D. Zucker, Physica A 287, 644 (2000)
F. Schweitzer, J.A. Holyst, Eur. Phys. J. B 15, 723 (2000)
V. Schwämmle, M.C. Gonzahles, A.A. Moreira, J.S. Andrade, H.J. Hermann, Phys. Rev. E 75, 066108 (2007)
H.P. McKean, Jr., PNAS 56, 1907 (1966)
H.P. McKean, Jr., in Lectures in differential equations, edited by A.K. Aziz (Van Nostrand Reinhold Company, New York, 1969), Vol. II, pp. 177–193
D.A. Dawson, J. Stat. Phys. 31, 29 (1983)
S. Meleard, S.R. Coppoletta, Stoch. proc. appl. 26, 317 (1987)
S. Meleard, in Probabilistic models for nonlinear partial differential equations, edited by C. Graham, T.G. Kurtz, S. Meleard, P.E. Potter, M. Pulvirenti, D. Talay (Springer, Berlin, 1996), pp. 42–95
T.D. Frank, Phys. Lett. A 372, 4553 (2008)
T.D. Frank, Phys. Lett. A 372, 6235 (2008)
T.D. Frank, J. Phys. A: Math. Gen. 41, 282001 (2008)
T.D. Frank, in Encyclopedia of Complexity and Systems Science, edited by R.A. Meyers (Springer, Berlin, 2009), Entry 764
T.D. Frank, Physica A 331, 391 (2004)
T.D. Frank, Nonlinear Fokker-Planck equations: Fundamentals and applications (Springer, Berlin,2005)
Y. Kuramoto, Chemical oscillations, waves, and turbulence (Springer, Berlin, 1984)
M. Shiino, Phys. Rev. A 36, 2393 (1987)
M. Shiino, Phys. Rev. E 67, 056118 (2003).
P.H. Chavanis, Phys. Rev. E 68, 036108 (2003)
P.H. Chavanis, Physica A 340, 57 (2004)
J.A. Acebron, L.L. Bonilla, C.J.P. Vicente, F. Ritort, R. Spigler, Rev. Mod. Phys. 77, 137 (2005)
V. Schwämmle, F.D. Nobre, E. Curado, Phys. Rev. E 76, 041123 (2007)
H. Hasegawa, Phys. Rev. E 67, 041903 (2003)
H. Hasegawa, Phys. Rev. E 68, 041909 (2003)
T.D. Frank, Eur. Phys. J. B 37, 139 (2004)
E.K. Lenzi, R.S. Mendes, K.S. Fa, L.S. Moraes, L.R. da Silva, L.S. Lucena, J. Math. Phys. 46, 083506(2005)
A.T. Silva, E.K. Lenzi, L.R. Evangelista, M.K. Lenzi, L.R. da Silva, Physica A 375, 65 (2007)
C. Tsallis, J. Stat. Phys. 52, 479 (1988)
A.R. Plastino, A. Plastino, Physica A 222, 347 (1995)
A. Compte, D. Jou, J. Phys. A: Math. Gen. 29, 4321 (1996)
T.D. Frank, A. Daffertshofer, Physica A 272, 497 (1999)
L. Borland, F. Pennini, A.R. Plastino, A. Plastino, Eur. Phys. J. B 12, 285 (1999)
L. Borland, Phys. Rev. Lett. 89, 098701 (2002)
L. Borland, J.P. Bouchaud, Quant. financ. 4, 499 (2004)
E.M.F. Curado, F.D. Nobre, Phys. Rev. E 67, 021107 (2003)
F.D. Nobre, E.M.F. Curado, G. Rowlands, Physica A 334, 109 (2004)
D.O. Kharchenko, V.O. Kharchenko, Physica A 354, 262 (2005)
M.A. Scarfone, T. Wada, Physica A 384, 305 (2007)
G.B. Bagci, A. Arda, R. Sever, Int. J. Mod. Phys. B 20, 2085 (2006)
G.B. Bagci, A. Arda, R. Sever, Mod. Phys. Lett. B 21, 981 (2007)
D.W. Strook, Markov processes from K. Ito’s perspective (Princton University Press, Princton, 2003)
V.N. Kolokoltsov, J. Stat. Phys. 126, 585 (2007)
Source: US house of representatives, www.house.gov, clerk.house.gov/evs/2008/roll681.xml, clerk.house.gov/evs/2008/roll674.xml
F. Reif, Fundamentals of statistical and thermal physics (McGraw-Hill Book Company, New York, 1965)
New York Times (Oct 4, 2008), www.nytimes.com/2008/10/04/business/economy/04bailout.html
F.J. Boster, J.E. Hunter, M.E. Mayer, J.L. Hale, in Communication Yearbook 4, edited by D. Nimmo (Transaction Books, New Brunswick, 1980), pp. 165–176
H. Haken, Synergetics: Introduction and advanced topics (Springer, Berlin, 2004)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Frank, T. Deterministic and stochastic components of nonlinear Markov models with an application to decision making during the bailout votes 2008 (USA). Eur. Phys. J. B 70, 249–255 (2009). https://doi.org/10.1140/epjb/e2009-00214-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2009-00214-4