TITLE

Bifurcations in nonstationarity noise dynamic systems: The basins of attraction and the problems of predictability of final states

AUTHOR(S)
Butkovskii, O. Ya.; Kravtsov, Yu. A.; Rychka, I. A.; Surovyatkina, E. D.
PUB. DATE
February 2000
SOURCE
AIP Conference Proceedings;2000, Vol. 502 Issue 1, p655
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
The properties of a connected time-varying system testing bifurcation of doubling of a phase are circumscribed. It is shown, that except for known properties of dynamic bifurcations (the violation of probability symmetry, the presence of a thin structure of the basins of attraction) the phenomenon of inversion of basins of attraction at transition of coefficient of connection through a critical value is also observed at the system. The essential dependance of phenomena on the coefficient of connection in a system is detected. © 2000 American Institute of Physics.
ACCESSION #
6028488

 

Related Articles

  • Use of hysteresis in bifurcation systems to measure noise. Butkovskiı, O. Ya.; Kravtsov, Yu. A.; Surovyatkina, E. D. // Technical Physics;Sep97, Vol. 42 Issue 9, p1099 

    It is proposed to make use of the influence of noise on the delay in dynamic bifurcations to measure the level of weak intrinsic noise in nonlinear chaotic systems. The dependence of the size of the hysteresis loop on the rate of change of the control parameter and on the noise level in a system...

  • Structure of the attraction zones of the final states in the presence of dynamical period doubling bifurcations. Butkovskiı, O. Ya.; Kravtsov, Yu. A.; Surovyatkina, E. D. // Journal of Experimental & Theoretical Physics;Jan98, Vol. 86 Issue 1, p206 

    The structure of the attraction zones of the final states associated with dynamical period doubling bifurcations is investigated. It is found that on the “initial value—transition rate” plane the attraction zones of the two possible final states alternate with each other and...

  • Prebifurcational Noise Rise in Nonlinear Systems. Kravtsov, Yu. A.; Bilchinskaya, S. G.; Butkovskii, O. Ya.; Rychka, I. A.; Surovyatkina, E. D. // Journal of Experimental & Theoretical Physics;Dec2001, Vol. 93 Issue 6, p1323 

    The phenomenon of prebifurcational noise increase in nonlinear systems in the process of perioddoubling bifurcation is investigated. The study is conducted for a discrete system (quadratic mapping); however, many of the laws discovered apply to more general systems. Estimates of the fluctuation...

  • Spontaneous movements and linear response of a noisy oscillator. J�licher, F.; Dierkes, K.; Lindner, B.; Prost, J.; Martin, P. // European Physical Journal E -- Soft Matter;Aug2009, Vol. 29 Issue 4, p449 

    A deterministic system that operates in the vicinity of a Hopf bifurcation can be described by a single equation of a complex variable, called the normal form. Proximity to the bifurcation ensures that on the stable side of the bifurcation ( i.e. on the side where a stable fixed point exists),...

  • Noise-induced current oscillations in superlattices: from stationary to moving domains. Schöll, Eckehard; Hizanidis, Johanne; Balanov, Alexander; Amann, Andreas // AIP Conference Proceedings;2007, Vol. 893 Issue 1, p543 

    We provide a detailed understanding of the transition between stationary and moving domains in semiconductor superlattices. We show that it corresponds to a global bifurcation (saddle-node infinite period bifurcation on a limit cycle or SNIPER). The dynamics close to such a bifurcation is...

  • ACTIVE BROWNIAN MOTION OF PAIRS AND SWARMS OF PARTICLES. Ebeling, W. // Acta Physica Polonica B;2007, Vol. 38 Issue 5, p1657 

    Following the route of Smoluchowski we continue the study of single active Brownian particles by investigations of the motion of pairs. After studying free motion we consider the relative motion of bound pairs. We study the attractor structure in a space of five dynamical variables. In...

  • GIANT SUPPRESSION OF THE ACTIVATION RATE IN DYNAMICAL SYSTEMS EXHIBITING CHAOTIC TRANSITIONS. Gac, Jakub M.; Zebrowski, Jan J. // Acta Physica Polonica B;2008, Vol. 39 Issue 5, p1019 

    The phenomenon of giant suppression of activation, when two or more correlated noise signals act on the system, was found a few years ago in dynamical bistable or metastable systems. When the correlation between these noise signals is strong enough and the amplitudes of the noise are chosen...

  • The effect of binary noise on a Hopf bifurcation. Binks, D. J.; Mullin, T.; Broomhead, D. S.; Nicol, M. // AIP Conference Proceedings;2000, Vol. 502 Issue 1, p247 

    We present the results of an experimental study of the effects of a adding a stochastic binary signal to the input of a nonlinear electronic oscillator. The circuit is a modified Van der Pol oscillator whose bifurcation structure is well understood. For high frequency digital noise added around...

  • Prebifurcation noise amplification and noise-dependent hysteresis as indicators of bifurcations in nonlinear geophysical systems. Surovyatkina, E.; Thiel, M. // Nonlinear Processes in Geophysics;2005, Vol. 12 Issue 1, p25 

    The phenomena of prebifurcation noise amplification and noise-dependent hysteresis are studied as prospective indicators of bifurcations ("noisy precursor") in nonlinear Geophysical systems. The phenomenon of prebifurcation noise amplification arises due to decreasing of damping coefficients...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics