TOOLS FOR DETECTING CHAOS

I n this study, useful tools for detecting chaos are explained. To observe the state variabtes (time series}, the phase portrait, the Poincare map, the power spectrum, the Lyapunov exponents and bifurcation diagram are used to detect chaos in dynamical systems. In this paper, the driven pendulum was choosen indicating chaos with the help of these tools. The existence of chaos in driven pendulum was shown with all methods. Simulation results obtained from all tools agree with each other. Also, control of chaos in driven pendulum was realized in this study
Anahtar Kelimeler:

chaos

___

  • Baker, G. L., Gollub, J. P.,. Chaotlc Dynamics an Jntroduction, Cambridge University Press, 1990.
  • Giannakopoulos, K., Dehyannis, T., Hadjidemetıiou, J.,. Means for Detecting Chaos and Hyperchaos İn Nonlinear Electronic Circuits,. DSP , 951 -954, 2002. Castillo, 0.,
  • Melin, P.,. Soft Computing for Control ofNon-linear Dynamical Systems, Phys1ca-Verlag, Strogatz, S. H.,. Nonlinear Dynamics and Chaos: with Applications to Phys1cs, Biology, Chemistry, and Engineering, Cambıidge Press, 1994.
  • Parker, T. S., Chua, L. 0.,. Practical Nunıeıical Algorithms for Chaotic Systenıs, Springer-Verlag, World Publlshing Corp. 1989. SAÜ Fen
  • Bilinıleri Enstitüsü Dergisi 9.Cilt, l Sayı Siu, S. W. K,. Lyapunov Exponent Toolbox, b/c on tr i b/v S/n1i 998. Tools For Detectıng Chaos- A.B. 01 '- Walter, J. M.,. The nonlİnear Pendulum project, University Of Ogata, I 998. Project:Pl Pyragas, K., Continuous Control of Chaos by Se If­ Control 1 ing Feedback, Physics Letter A, 1992