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Simple environment for developing methods of controlling chaos in spatially distributed systems Cover

Simple environment for developing methods of controlling chaos in spatially distributed systems

By: Łukasz Korus  
Open Access
|Mar 2011

References

  1. Alsing, P. M., Gavrielides, A. and Kovanis, V. (1994). Using neural networks for controling chaos, Physical Review E 49(2): 1225-1231.10.1103/PhysRevE.49.1225
  2. Andrievskii, B. R. and Fradkov, A. L. (2003). Control of chaos: Methods and applications, Automation and Remote Control 64(5): 673-713.10.1023/A:1023684619933
  3. Andrzejak, R. G., Lehnertz, K., Mormann, F., Rieke, C., David, P. and Elger, C. E. (2001). Indications of nonlinear deterministic and finite-dimensional structures in time series of brain electrical activity: Dependence on recording region and brain state, Physical Review E 64(1): 1-8.10.1103/PhysRevE.64.06190711736210
  4. Argoul, F., Arneodo, A., Richetti, P. and Roux, J. C. (1987). From quasiperiodicity to chaos in the Belousov-Zhabotinskii reaction, I: Experiment, Journal of Chemical Physics 86(6): 3325-3339.10.1063/1.452751
  5. Astakhov, V. V., Anishchenko, V. S. and Shabunin, A. V. (1995). Controlling spatiotemporal chaos in a chain of the coupled logostic maps, IEEE Transactions on Circuits and Systems 42(6): 352-357.10.1109/81.390267
  6. Auerbach, D. (1994). Controlling extended systems of chaotic elements, Physical Review Letters 72(8): 1184-1187.10.1103/PhysRevLett.72.118410056644
  7. Banerjee, S., Misra, A. P., Shukla, P. K. and Rondoni, L. (2010). Spatiotemporal chaos and the dynamics of coupled langmuir and ion-acoustic waves in plasmas, Physical Review E 81(1): 1-10.10.1103/PhysRevE.81.04640520481845
  8. Beck, O., Amann, A., Scholl, E., Socolar, J. E. S. and Just, W. (2002). Comparison of time-delay feedback schemes for spatiotemporal control of chaos in a reaction-diffusion system with global coupling, Physical Review E 66(1): 1-6.10.1103/PhysRevE.66.01621312241467
  9. Boukabou, A. and Mansouri, N. (2005). Predictive control of higher dimensional chaos, Nonlinear Phenomena in Complex Systems 8(3): 258-265.
  10. Chen, G. and Dong, X. (1993). On feedback control of chaotic continuous-time systems, IEEE Transactions on Circuits and Systems 40(9): 591-601.10.1109/81.244908
  11. Chopard, B., Dupuis, A., Masselot, A. and Luthi, P. (2002). Cellular automata and lattice Boltzmann techniques: An approach to model and simulate complex systems, Advances in Complex Systems 5(2): 103-246.10.1142/S0219525902000602
  12. Chui, S. T. and Ma, K. B. (1982). Nature of some chaotic states for Duffing's equation, Physical Review A 26(4): 2262-2265.10.1103/PhysRevA.26.2262
  13. Córdoba, A., Lemos, M. C. and Jiménez-Morales, F. (2006). Periodical forcing for the control of chaos in a chemical reaction, Journal of Chemical Physics 124(1): 1-6.10.1063/1.214195716409051
  14. Crutchfield, J. P. and Kaneko, K. (1987). Directions in Chaos. Phenomenology of Spatio-Temporal Chaos, World Scientific Publishing Co., Singapore.
  15. Dressler, U. and Nitsche, G. (1992). Controlling chaos using time delay coordinates, Physical Review Letters 68(1): 1-4.10.1103/PhysRevLett.68.110045097
  16. Gautama, T., Mandic, D. P. and Hulle, M. M. V. (2003). Indications of nonlinear structures in brain electrical activity, Physical Review E 67(1): 1-5.10.1103/PhysRevE.67.04620412786457
  17. Govindan, R. B., Narayanan, K. and Gopinathan, M. S. (1998). On the evidence of deterministic chaos in ECG: Surrogate and predictability analysis, Chaos 8(2): 495-502.10.1063/1.16633012779752
  18. Greilich, A. and Markus, M. (2003). Correlation of entropy with optimal pinning density for the control of spatiotemporal chaos, Nonlinear Phenomena in Complex Systems 6(1): 541-546.
  19. Gunaratne, G. H., Lisnay, P. S. and Vinson, M. J. (1989). Chaos beyond onset: A comparison of theory and experiment, Physical Review Letters 63(1): 1-4.10.1103/PhysRevLett.63.110040417
  20. Held, G. A., Jeffries, C. and Haller, E. E. (1984). Observation of chaotic behavior in an electron-hole plasma in GE, Physical Review Letters 52(12): 1037-1040.10.1103/PhysRevLett.52.1037
  21. Jacewicz, P. (2002). Model Analysis and Synthesis of Complex Physical Systems Using Cellular Automata, Ph.D. thesis, University of Zielona Góra, Zielona Góra.
  22. Kaneko, K. (1990). Simulating Physics with Coupled Map Lattices, World Scientific Publishing Co., Singapore.
  23. Korus, L. (2007). Alternative methods of wave motion modelling, in B. Apolloni, R. J. Howlett and L. Jain (Eds.) Knowledge-Based Intelligent Information and Engineering Systems: KES2007/WIRN2007, Part 1, Lecture Notes in Artificial Intelligence, Vol. 4692, Springer-Verlag, Berlin/Heidelberg, pp. 335-345.10.1007/978-3-540-74819-9_42
  24. Kwon, Y. S., Ham, S. W. and Lee, K. K. (1997). Analysis of minimal pinning density for controlling spatiotemporal chaos of a coupled map lattice, Physical Review E 55(2): 2009-2012.10.1103/PhysRevE.55.2009
  25. Langenberg, J., Pfister, G. and Abshagen, J. (2004). Chaos from Hopf bifurcation in a fluid flow experiment, Physical Review E 70(4): 046209.10.1103/PhysRevE.70.04620915600497
  26. Mihaliuk, E., Sakurai, T., Chirila, F. and Showalter, K. (2002). Feedback stabilization of unstable propagating waves, Physical Review E 65(6): 065602.10.1103/PhysRevE.65.06560212188776
  27. Ott, E. (2002). Chaos in Dynamical Systems, Cambridge University Press, Cambridge.10.1017/CBO9780511803260
  28. Ott, E., Grebogi, C. and Yorke, J. A. (1990). Controlling chaos, Physical Review Letters 64(11): 1196-1199.10.1103/PhysRevLett.64.119610041332
  29. Parekh, N., Parthasarathy, S. and Sinha, S. (1998). Global and local control of spatiotemporal chaos in coupled map lattice, Physical Review Letters 81(7): 1401-1404.10.1103/PhysRevLett.81.1401
  30. Parmananda, P. (1997). Controlling turbulence in coupled map lattice systems using feedback techniques, Physical Review E 56(1): 239-244.10.1103/PhysRevE.56.239
  31. Procaccia, I. and Meron, E. (1986). Low-dimensional chaos in surface waves: Theoretical analysis of an experiment, Physical Review A 34(4): 3221-3237.10.1103/PhysRevA.34.32219897641
  32. Pyragas, K. (2001). Control of chaos via an unstable delayed feedback controller, Physical Review Letters 86(11): 2265-2268.10.1103/PhysRevLett.86.226511289905
  33. Singer, J., Wang, Y. and Haim, H. B. (1991). Controlling a chaotic system, Physical Review Letters 66(9): 1123-1125.10.1103/PhysRevLett.66.112310044001
  34. Used, J. and Martin, J. C. (2010). Multiple topological structures of chaotic attractors ruling the emission of a driven laser, Physical Review E 82(1): 016218.10.1103/PhysRevE.82.01621820866718
  35. Wei, W., Zonghua, L. and Bambi, H. (2000). Phase order in chaotic maps and in coupled map lattices, Physical Review Letters 84(12): 2610-2613.10.1103/PhysRevLett.84.261011017281
  36. Weimar, J. R. (1997). Simulation with Cellular Automata, Logos Verlang Berlin, Berlin.
  37. Yamada, T. and Graham, R. (1980). Chaos in a laser system under a modulated external field, Physical Review Letters 45(16): 1322-1324.10.1103/PhysRevLett.45.1322
  38. Yim, G., Ryu, J., Park, Y., Rim, S., Lee, S., Kye, W. and Kim, C. (2004). Chaotic behaviors of operational amplifiers, Physical Review E 69(4): 045201.10.1103/PhysRevE.69.04520115169058
  39. Zhu, K. and Chen, T. (2001). Controlling spatiotemporal chaos in coupled map lattice, Physical Review E 63(3): 067201.10.1103/PhysRevE.63.06720111415259
DOI: https://doi.org/10.2478/v10006-011-0011-4 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 149 - 159
Published on: Mar 28, 2011
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2011 Łukasz Korus, published by University of Zielona Góra
This work is licensed under the Creative Commons License.

Volume 21 (2011): Issue 1 (March 2011)