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Energy-optimal steering of transitions through a fractal basin boundary.

By A. N. Silchenko, S. Beri, D. G. Luchinsky and Peter V. E. McClintock

Abstract

We study fluctuational transitions in a discrete dy- namical system having two co-existing attractors in phase space, separated by a fractal basin boundary. It is shown that transitions occur via a unique ac- cessible point on the boundary. The complicated structure of the paths inside the fractal boundary is determined by a hierarchy of homoclinic original sad- dles. By exploiting an analogy between the control problem and the concept of an optimal fluctuational path, we identify the optimal deterministic control function as being equivalent to the optimal fluctu- ational force obtained from a numerical analysis of the fluctuational transitions between two states

Publisher: IEEE
Year: 2004
OAI identifier: oai:eprints.lancs.ac.uk:31486
Provided by: Lancaster E-Prints

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Citations

  1. (1979). A nonlinear oscillator with a strange attractor,”
  2. (1979). A nonlinear oscillator with a strange attractor,"
  3. (1987). Activation energy for thermally induced escape from a basin of attraction,”
  4. (1987). Activation energy for thermally induced escape from a basin of attraction,"
  5. (1998). Analogue studies of nonlinear systems,”
  6. (1998). Analogue studies of nonlinear systems,"
  7. (1987). Basin boundaries metamorphoses - changes in accessible boundary orbits,” doi
  8. (1987). Basin boundaries metamorphoses - changes in accessibleboundary orbits,"
  9. (1994). Controlling chaos experimentally in systems exhibiting large effective Lyapunov exponents,”
  10. (1994). Controlling chaos experimentally in systems exhibiting large effective Lyapunov exponents,"
  11. (1995). E±cient switching between controlled unstable periodic orbits in higher dimensional chaotic systems,"
  12. (1995). Efficient switching between controlled unstable periodic orbits in higher dimensional chaotic systems,”
  13. (1978). Exit probabilities and stochastic control,”
  14. (1978). Exit probabilities and stochastic control,"
  15. (1997). Experiments on critical phenomena in anoisy exit problem,”
  16. (1997). Experiments on critical phenomena in anoisy exit problem,"
  17. (1983). Final-state sensitivity - an obstruction of predictability,” doi
  18. (1983). Final-state sensitivity - an obstruction of predictability,"
  19. (1999). Fluctuationinduced escape from the basin of attraction of a quasiattractor,”
  20. (1999). Fluctuationinduced escape from the basin of attraction of a quasiattractor,"
  21. (1953). Fluctuations and irreversible processes,”
  22. (1953). Fluctuations and irreversible processes,"
  23. (1985). Fractal basin boundaries,"
  24. (1998). Introduction to Control of Oscillations and Chaos,
  25. (1969). Lectures on the Calculus of Variations and Optimal Control Theory,
  26. (1997). Migration control in two coupled Du±ng oscillators,"
  27. (1997). Migration control in two coupled Duffing oscillators,”
  28. (1989). Noise-induced escape from attractor in one-dimensional maps,”
  29. (1989). Noise-induced escape from attractor in one-dimensional maps,"
  30. (1989). Noise-induced escape from attractors,”
  31. (1989). Noise-induced escape from attractors,"
  32. Noise-induced escape through a fractal basin boundaries,” Physica A, to be published. doi
  33. Noise-induced escape through a fractal basin boundaries," Physica A, to be published.
  34. (1991). Nonequilibrium potentials for dynamical systems with fractal attractors or repellers,”
  35. (1991). Nonequilibrium potentials for dynamical systems with fractal attractors or repellers,"
  36. (1992). Optimal paths and the prehistory problemfor large °uctuations in noise driven systems,"
  37. (1992). Optimal paths and the prehistory problemfor large fluctuations in noise driven systems,”
  38. (1997). Optimal timing for targeting periodic orbits in a loss-driven CO2 laser,” doi
  39. (1997). Optimal timing for targeting periodic orbits in a loss-driven CO2 laser,"
  40. (1984). Random Perturbations in Dynamical Systems,
  41. (2001). Strong enhancement of noiseinduced escape by nonadiabatic periodic driving due to transient chaos,”
  42. (2001). Strong enhancement of noiseinduced escape by nonadiabatic periodic driving due to transient chaos,"
  43. (2002). The natural measure of nonattracting chaotic sets and its representation by unstable periodic orbits,” doi
  44. (2002). The natural measure of nonattracting chaotic sets and its representation by unstable periodic orbits,"
  45. (1997). The OPCL control method for entrainment, model-resonance, and migration actions on multiple-attractor systems,”
  46. (1997). The OPCL control method for entrainment, model-resonance, and migration actions on multiple-attractor systems,"
  47. (1988). Unstable periodic orbits and the dimensions of multifractal chaotic attractors,” doi
  48. (1988). Unstable periodic orbits and the dimensions of multifractal chaotic attractors,"
  49. (1993). Using small perturbations to control chaos,”
  50. (1993). Using small perturbations to control chaos,"

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