Fractal Approach, Bifurcation Poker and Suc-Logic for Nonlinear Dynamics Forecasting

作者: YURY KOLOKOLOV , ANNA MONOVSKAYA

DOI: 10.1142/S0218127413502015

关键词: Applied mathematicsNonlinear systemMathematicsBifurcationStability marginMeaning (existential)Artificial intelligenceFractal

摘要: The paper is devoted to the novel logic (SUC-logic) of nonlinear dynamics forecasting. SUC-logic based on three main points: special sections (S) build 2D projections multidimensional spaces without loss useful information; units (U) measurement estimate evolution; consecutions (C) realize forecasting step-by-step. fractal approach in real-time together with modified bifurcation diagrams research regularities and uncertainties evolution scenarios are developed SUC-logic. physical meaning uncertainty zone, stability margin, risk estimation, farthest earliest considered from viewpoint aspect. Reasonings discussions experimental computational results.

参考文章(50)
Laurette Tuckerman, Yves Pomeau, Christian Vidal, Pierre Bergé, David Ruelle, Order within chaos : towards a deterministic approach to turbulence Wiley , Hermann. ,(1984)
Y.V. Kolokolov, S.L. Koschinsky, V.V. Bagrov, Experimental dynamics of electromechanical pulse energy conversion systems IEEE Transactions on Instrumentation and Measurement. ,vol. 55, pp. 35- 43 ,(2006) , 10.1109/TIM.2005.862007
A. Venkatesan, S. Parthasarathy, M. Lakshmanan, Occurrence of multiple period-doubling bifurcation route to chaos in periodically pulsed chaotic dynamical systems Chaos Solitons & Fractals. ,vol. 18, pp. 891- 898 ,(2003) , 10.1016/S0960-0779(03)00092-4
Witold Pedrycz, Andrzej Bargiela, Fuzzy fractal dimensions and fuzzy modeling Information Sciences. ,vol. 153, pp. 199- 216 ,(2003) , 10.1016/S0020-0255(03)00075-6
Yury V. Kolokolov, Anna V. Monovskaya, Abdelaziz Hamzaoui, On-line identification of multidimensional parametric vector random variation of pulse system Chaos, Solitons & Fractals. ,vol. 24, pp. 825- 838 ,(2005) , 10.1016/J.CHAOS.2004.09.078
Qiaolin Yuan, Barry Lennox, Matthew McEwan, Analysis of multivariable control performance assessment techniques Journal of Process Control. ,vol. 19, pp. 751- 760 ,(2009) , 10.1016/J.JPROCONT.2008.10.001
A. Talha Yalta, Olaf Jenal, On the importance of verifying forecasting results International Journal of Forecasting. ,vol. 25, pp. 62- 73 ,(2009) , 10.1016/J.IJFORECAST.2008.07.002
Yu. V. Kolokolov, A. V. Monovskaya, Preventive diagnosis of pulse power converter dynamics Automation and Remote Control. ,vol. 70, pp. 1228- 1242 ,(2009) , 10.1134/S0005117909070133