Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Statistical properties of dynamical chaos

1. Institute of Nonlinear Dynamics, Department of Physics, Saratov State University, 83, Astrakhanskaya str., 410012, Saratov

   

This study presents a survey of the results obtained by the authors on statistical description of dynamical chaos and the e ffect of noise on dynamical regimes. We deal with nearly hyperbolic and nonhyperbolic chaotic attractors and discuss methods of diagnosing the type of an attractor. We consider regularities of the relaxation to an invariant probability measure for diff erent types of attractors. We explore peculiarities of autocorrelation decay and of power spectrum shape and their interconnection with Lyapunov exponents, instantaneous phase di ffusion and the intensity of external noise. Numeric results are compared with experimental data.
  Figure/Table
  Supplementary
  Article Metrics

Keywords e ffective diff usion coefficient.; phase variance; nonhyperbolic attractors; spiral and funnel chaos; autocorrelation function; instantaneous phase

Citation: Vadim S. Anishchenko, Tatjana E. Vadivasova, Galina I. Strelkova, George A. Okrokvertskhov. Statistical properties of dynamical chaos. Mathematical Biosciences and Engineering, 2004, 1(1): 161-184. doi: 10.3934/mbe.2004.1.161

 

This article has been cited by

  • 1. Dong-Wei Huang, Hong-Li Wang, Jian-Feng Feng, Zhi-Wen Zhu, Modelling algal densities in harmful algal blooms (HAB) with stochastic dynamics, Applied Mathematical Modelling, 2008, 32, 7, 1318, 10.1016/j.apm.2007.04.006
  • 2. Dongwei Huang, Hongli Wang, Jianfeng Feng, Zhi-wen Zhu, Hopf bifurcation of the stochastic model on HAB nonlinear stochastic dynamics, Chaos, Solitons & Fractals, 2006, 27, 4, 1072, 10.1016/j.chaos.2005.04.086
  • 3. , , Lozi Mappings, 2013, 263, 10.1201/b15363-7
  • 4. V S Anishchenko, G A Okrokvertskhov, T E Vadivasova, G I Strelkova, Mixing and spectral-correlation properties of chaotic and stochastic systems: numerical and physical experiments, New Journal of Physics, 2005, 7, 76, 10.1088/1367-2630/7/1/076
  • 5. Oliver K. Ernst, Thomas M. Bartol, Terrence J. Sejnowski, Eric Mjolsness, Learning moment closure in reaction-diffusion systems with spatial dynamic Boltzmann distributions, Physical Review E, 2019, 99, 6, 10.1103/PhysRevE.99.063315

Reader Comments

your name: *   your email: *  

Copyright Info: 2004, Vadim S. Anishchenko, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved