Abstract
Real systems are subjected to certain amount of unavoidable internal or external random perturbations, usually termed as noise. The presence of noise is not only unavoidable in electrical and electronic devices, but it can significantly affect their performance. As pointed out in the beginning of Chap. 2, a variety of phenomena can be induced by the presence of noise. An oscillating system in which noise is significant and is the source of its oscillatory dynamics, then it is generally called an stochastic oscillator. A mathematical model of such a system in the absence of noise and external periodic force does not exhibit any kind of oscillatory motion. A stochastic oscillator can be monostable, multistable or excitable. In certain cases the effect of noise in a stochastic oscillator is nontrivial. That is, the increase of noise intensity need not always increase the irregularity of the response. An appropriate weak noise can give rise to a maximum coherence similar to the stochastic resonance but in the absence of any external periodic force.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
H. Gang, T. Ditzinger, C.Z. Ning, H. Haken, Phys. Rev. Lett. 71, 807 (1993)
A.S. Pikovsky, J. Kurths, Phys. Rev. Lett. 78, 775 (1997)
B. Linder, L. Schimanwky-Geier, Phys. Rev. E 61, 6103 (2000)
C. Palenzuela, R. Toral, C.R. Mirasso, O. Calvo, J.D. Gunton, Europhys. Lett. 56, 347 (2001)
E. Ippen, J. Lindner, W.L. Ditto, J. Stat. Phys. 70, 437 (1993)
S. Zambrano, J.M. Casado, M.A.F. Sanjuan, Phys. Lett. A 366, 428 (2007)
S. Arathi, S. Rajasekar, J. Kurths, Int. J. Bifurcation Chaos 23, 1350132 (2013)
W.J. Rappel, S.H. Strogatz, Phys. Rev. E 50, 3249 (1994)
Z. Liu, Y. Lai, Phys. Rev. Lett. 86, 4737 (2001)
J.D. Murray, Mathematical Biology (Springer, Berlin, 1993)
M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970)
P.M. Gade, R. Rai, H. Singh, Phys. Rev. E 56, 2518 (1997)
K.T. Alligood, T.D. Sauer, J.A. Yorke, Chaos, an Introduction to Dynamical Systems (Springer, New York, 1996)
W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in Fortran, Indian edition (Foundation Books, New Delhi, 1993)
G.E.P. Box, M.E. Muller, Ann. Math. Stat. 29, 610 (1958)
E. Ott, C. Grebogi, J.A. Yorke, Phys. Rev. Lett. 64, 1196 (1990)
F. Borgogno, P. D’odorico, F. Laio, L. Ridolfi, J. Theor. Biol. 293, 65 (2012)
M. Sieber, H. Malchow, L. Schimanksy-Geier, Ecol. Complex. 4, 223 (2007)
G. Giacomelli, M. Giudici, S. Balle, J.R. Tredice, Phys. Rev. Lett. 84, 3298 (2000)
K. Mujakawa, H. Isikawa, Phys. Rev. E 66, 046204 (2002)
A. Kolbus, A. Lemarchand, A.L. Kawcyzynski, B. Nowakowski, Phys. Chem. 12, 13224 (2010)
V.P. Munuzuri, R. Deza, K. Fraedrich, T. Kunz, F. Lunkeit, Phys. Rev. E 71, 065602 (2005)
O. Carrillo, M.A. Santos, G. Garcia-Ojalvo, J.M. Sancho, Europhys. Lett. 65, 452 (2004)
C.Y. Lee, W. Choi, J.H. Han, M.S. Strano, Science 329, 1320 (2010)
M. Gosak, M. Perc, Phys. Rev. E 76, 037201 (2007)
C.S. Zhou, J. Kurths, B. Hu, Phys. Rev. Lett. 87, 098101 (2001)
C.S. Zhou, J. Kurths, Chaos 13, 401 (2003)
H.S. Wio, Phys. Rev. E 54, R3075 (1995)
S.K. Han, T.G. Yim, D.E. Postrov, O.V. Sosnovtseva, Phys. Rev. Lett. 83, 1771 (1999)
Z. Liu, Y.C. Lai, Phys. Rev. Lett. 86, 4737 (2001)
Y.C. Lai, Z. Liu, Phys. Rev. E 64, 066202 (2001)
M. Zhan, G.W. Wei, C.H. Lai, Y.C. Lai, Z. Liu, Phys. Rev. E 66, 036201 (2002)
M. Perc, Chaos Solitons Fractals 31, 64 (2007)
M. Gosak, M. Marhl, M. Perc, Biophys. Chem. 128, 210 (2007)
A. Zakharova, T. Vadivasova, V. Anishchenko, A. Koseska, J. Kurths, Phys. Rev. E 81, 011106 (2010)
C. Otto, B. Lingnau, E. Scholl, K. Ludge, Opt. Exp. 22, 13288 (2014)
J. Rajhans, A.N. Sekar Iyengar (1 Dec 2013). arXiv:1312.02031v1 [nlin.CD]
M. Gosak, D. Korosak, M. Marhl, Phys. Rev. E 81, 056104 (2010)
S. Biswas, D. Das, P. Parmananda, A. Sain, Phys. Rev. E 80, 046220 (2009)
Y. Jim, H. Hu, Physica A 382, 423 (2007)
M.A. Arteaga, M. Valencia, M. Sciamana, H. Thienpont, M. Lopez-Amo, K. Panajotov, Phys. Rev. Lett. 99, 023903 (2007)
R. Aust, P. Hovel, J. Hizanidis, E. Scholl, Eur. Phys J. Special Topics 187, 77 (2010)
T. Tang, Y. Jia, M. Yi, J. Ma, J. Li, Phys. Rev. E 77, 061905 (2008)
Y. Gong, Y. Xie, Y. Hao, J. Chem. Phys. 130, 165106 (2009)
V. Beato, I.S. Nadal, I. Gerdes, H. Enge, Phil. Trans R. Soc. A 366, 381 (2008)
A. Zakharova, A. Feoktistov, T. Vadivasova, E. School, Eur. Phys. J. Special Topics 222, 2481 (2013)
M. Perc, M. Marhl, Phys. Rev. E 73, 066205 (2006)
X. Lin, Y. Gong, L. Wang, Chaos 21, 043109 (2011)
X. Sun, M. Perc, Q. Lu, J. Kurths, Chaos 18, 023102 (2008)
M. Perc, Chaos Solitons Fractals 31, 280 (2007)
M. Perc, New J. Phys. 7, 252 (2005)
C. Men, J. Wang, Y.M. Qin, B. Deng, K.M. Tsang, W.L. Chan, Chaos 22, 013104 (2012)
O. Calvo, C.R. Mirasso, R. Toral, Elect. Lett. 37, 1062 (2001)
Y. Li, J. Rinzel, J. Theor. Biol. 166, 461 (1994)
J.W. Shuai, P. Jung, Phys. Rev. Lett. 88, 068102 (2002)
Y. Morishita, T.J. Kobayashi, K. Aihara, Biophys. J. 91, 2072 (2006)
Z.H. Hou, J.Q. Zhang, H.W. Xin, Phys. Rev. E 74, 031901 (2006)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Rajasekar, S., Sanjuan, M.A.F. (2016). Coherence and Chaotic Resonances. In: Nonlinear Resonances. Springer Series in Synergetics. Springer, Cham. https://doi.org/10.1007/978-3-319-24886-8_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-24886-8_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-24884-4
Online ISBN: 978-3-319-24886-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)