Loading [Contrib]/a11y/accessibility-menu.js

Mathematical Biosciences and Engineering

Search Advanced

Mathematical Biosciences and Engineering

2004, Volume 1, Issue 1: 161-184. doi: 10.3934/mbe.2004.1.161

Previous Article Next Article

Statistical properties of dynamical chaos

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

Received: 01 January 2004 Accepted: 29 June 2018 Published: 01 March 2004
MSC : 92D30.

This study presents a survey of the results obtained by the authors on statistical description of dynamical chaos and the effect 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 different types of attractors. We explore peculiarities of autocorrelation decay and of power spectrum shape and their interconnection with Lyapunov exponents, instantaneous phase diffusion and the intensity of external noise. Numeric results are compared with experimental data.

Keywords:

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

Related Papers:

[1]	Juvencio Alberto Betancourt-Mar, José Manuel Nieto-Villar . Theoretical models for chronotherapy: Periodic perturbations in funnel chaos type. Mathematical Biosciences and Engineering, 2007, 4(2): 177-186. doi: 10.3934/mbe.2007.4.177
[2]	Zigen Song, Jian Xu, Bin Zhen . Mixed-coexistence of periodic orbits and chaotic attractors in an inertial neural system with a nonmonotonic activation function. Mathematical Biosciences and Engineering, 2019, 16(6): 6406-6425. doi: 10.3934/mbe.2019320
[3]	E.V. Presnov, Z. Agur . The Role Of Time Delays, Slow Processes And Chaos In Modulating The Cell-Cycle Clock. Mathematical Biosciences and Engineering, 2005, 2(3): 625-642. doi: 10.3934/mbe.2005.2.625
[4]	V. Volpert, B. Xu, A. Tchechmedjiev, S. Harispe, A. Aksenov, Q. Mesnildrey, A. Beuter . Characterization of spatiotemporal dynamics in EEG data during picture naming with optical flow patterns. Mathematical Biosciences and Engineering, 2023, 20(6): 11429-11463. doi: 10.3934/mbe.2023507
[5]	Xiaoling Han, Xiongxiong Du . Dynamics study of nonlinear discrete predator-prey system with Michaelis-Menten type harvesting. Mathematical Biosciences and Engineering, 2023, 20(9): 16939-16961. doi: 10.3934/mbe.2023755
[6]	Jorge Duarte, Cristina Januário, Nuno Martins . A chaotic bursting-spiking transition in a pancreatic beta-cells system: observation of an interior glucose-induced crisis. Mathematical Biosciences and Engineering, 2017, 14(4): 821-842. doi: 10.3934/mbe.2017045
[7]	John E. Franke, Abdul-Aziz Yakubu . Periodically forced discrete-time SIS epidemic model with disease induced mortality. Mathematical Biosciences and Engineering, 2011, 8(2): 385-408. doi: 10.3934/mbe.2011.8.385
[8]	Yi Yang, Lirong Liu, Changcheng Xiang, Wenjie Qin . Switching dynamics analysis of forest-pest model describing effects of external periodic disturbance. Mathematical Biosciences and Engineering, 2020, 17(4): 4328-4347. doi: 10.3934/mbe.2020239
[9]	Huidong Cheng, Hui Xu, Jingli Fu . Dynamic analysis of a phytoplankton-fish model with the impulsive feedback control depending on the fish density and its changing rate. Mathematical Biosciences and Engineering, 2023, 20(5): 8103-8123. doi: 10.3934/mbe.2023352
[10]	Jie Lou, Tommaso Ruggeri, Claudio Tebaldi . Modeling Cancer in HIV-1 Infected Individuals: Equilibria, Cycles and Chaotic Behavior. Mathematical Biosciences and Engineering, 2006, 3(2): 313-324. doi: 10.3934/mbe.2006.3.313

Abstract

This study presents a survey of the results obtained by the authors on statistical description of dynamical chaos and the effect 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 different types of attractors. We explore peculiarities of autocorrelation decay and of power spectrum shape and their interconnection with Lyapunov exponents, instantaneous phase diffusion and the intensity of external noise. Numeric results are compared with experimental data.

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, 2008, 32, 0307904X, 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, 2006, 27, 09600779, 1072, 10.1016/j.chaos.2005.04.086
3.	2013, 978-1-4665-8070-1, 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, 2005, 7, 1367-2630, 76, 10.1088/1367-2630/7/1/076
5.	Mohammed F. Daqaq, Rafael S. Crespo, Sohmyung Ha, On the efficacy of charging a battery using a chaotic energy harvester, 2020, 99, 0924-090X, 1525, 10.1007/s11071-019-05372-0
6.	Oliver K. Ernst, Thomas M. Bartol, Terrence J. Sejnowski, Eric Mjolsness, Learning moment closure in reaction-diffusion systems with spatial dynamic Boltzmann distributions, 2019, 99, 2470-0045, 10.1103/PhysRevE.99.063315

Reader Comments

Your name:*

Email:*
© 2004 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Mathematical Biosciences and Engineering

4.4

Metrics

Article views(3936) PDF downloads(906) Cited by(6)

Export Citation

Article outline

Show full outline

Other Articles By Authors

On This Site
On Google Scholar

/

DownLoad: Full-Size Img PowerPoint