Optimal fluctuations and the control of chaos

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 12, Issue 3, 2002, Pages 583-604

  Luchinsky, D G ^a,b   Beri, S ^b   Mannella, R ^b   McClintock, P V E ^a,b   Khovanov, I A ^c  

^a LANCASTER UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF PISA   (Italy)

^c SARATOV STATE UNIVERSITY   (Russian Federation)

Author keywords

Control of chaos; Escape; Large fluctuations; Nonlinear oscillator; Optimal control; Optimal force; Optimal path; Stochastic process

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; CONTROL SYSTEMS; FUNCTIONS; HAMILTONIANS; OPTIMIZATION; PROBLEM SOLVING; RANDOM PROCESSES; STATISTICAL METHODS;

OPTIMAL FLUCTUATIONS;

CHAOS THEORY;

EID: 0036011528     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127402004528     Document Type: Article

References (66)

1. Influence of noise on statistical properties of nonhyperbolie attractors
2. The Kramers problem for a multi-well potential
3. Exploring chaotic motion through periodic orbits
4. Efficient switching between controlled unstable periodic orbits in higher dimensional chaotic systems
5. Noise-induced escape from attractor in one-dimensional maps
6. The control of chaos: Theory and applications
7. On the numerical integration of nonlinear two-point boundary value problems using iterated deferred corrections, part 1: A survey and comparison of some one-step formulae
8. On the numerical integration of nonlinear two-point boundary value problems using iterated deferred corrections, part 2: The development and analysis of highly stable deferred correction formulae
9. Implementation issues in solving nonlinear equations for twopoint boundary value problems
10. A deferred correction method for nonlinear two-point boundary-valueproblems: Implementation and numerical evaluation
11. 2 laser
12. 2 laser
13. 2 laser response to loss perturbation near period doubling
14. Unstable periodic orbits and the natural measure of nonhyperbolic chaotic saddles
15. Dynamic programming and the calculus of variations
16. Theory of nonlinear oscillator interacting with a medium
17. Optimal paths and the prehistory problem for large fluctuations in noise driven systems
18. Observable and hidden features of large fluctuations in nonequilibrium systems
19. Large fluctuations and optimal paths in chemical kinetics
20. Corrals and critical behavior of the distribution of fluctuational paths
21. Resonant directed diffusion in nonadiabatically driven systems
22. Use of Hamiltonian mechanics in systems driven by colored noise
23. Multistability and control of complexity
24. Dynamical properties of a simple mechanical system with a large number of coexisting periodic attractors
25. Exit probabilities and stochastic control
26. Learning to control a complex multistable system
27. Existence of a potential for dissipative dynamical systems
28. Nonequilibrium potentials for dynamical systems with fractal attractors or repellers
29. Noise-induced escape from attractors
30. Unstable periodic orbits and the dimensions of multifractal chaotic attractors
31. Optimal control
32. Controlling chaos experimentally in systems exhibiting large effective Lyapunov exponents
33. The OPCL control methods for entrainment, model-resonance, and migration actions on multiple-attractor systems
34. Nondifferentiable potentials for nonequilibrium steady states
35. Activation energy for thermally induced escape from a basin of attraction
36. Fluctuations and the energy-optimal control of chaos
37. Fluctuational escape from a chaotic attractor
38. A discrete-time version of the Wentzel-Friedlin theory
39. Large deviations in dynamical systems and stochastic processes
40. Preference of attractors in noisy multistable systems
41. Zero-dispersion nonlinear resonance in dissipative systems
42. On the nature of large fluctuations in equilibrium systems: Observation of an optimal force
43. Irreversibility of classical fluctuations studied in analogue electrical circuits
44. Analogue studies of nonlinear systems
45. Fluctuation-induced escape from the basin of attraction of a quasiattractor
46. Observation of saddle-point avoidance in noise-induced escape
47. Escape problem for irreversible systems
48. A scaling theory of bifurcations in the symmetric weak-noise escape problem
49. Limiting exit location distributions in the stochastic exit problem
50. A fast, easily implemented method for sampling from decreasing or symmetric unimodal density-functions
51. Fluctuations and irreversible processes
52. Migration control in two coupled Duffing oscillators
53. Detecting unstable periodic orbits of chaotic dynamical systems
54. Using chaos to direct trajectories to targets
55. Using small perturbations to control chaos
56. Progress in the control of chaos
57. Calculations of periodic orbits: The monodromy method and application to regularized systems
58. Optimal control of large fluctuations
59. Topological features of large fluctuations to the interior of a limit cycle
60. Zero-dispersion nonlinear resonance
61. Nonlinear generalized Langevin equations