Controlling chaos.¶
Ott, E., Grebogi, C., & Yorke, J. A. (1990). Controlling chaos. Physical Review Letters, 64(11), 1196-1199.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Attractor Selection and Basin Control
- The key insight, formalized by Ott, Grebogi, and Yorke (1990) in their seminal work on controlling chaos, is that control becomes not a matter of forcing an impossible transition to any arbitrary state, but rather a strategic shift of the basins themselves—the regions of state-space that lead to each attractor—so that the system's natural dynamics carry it toward a desired outcome.
This sourceSeminal OGY method: control of a system by small time-dependent parameter perturbations that exploit the system's own dynamics (stabilizing unstable orbits / steering toward target states) rather than large direct forcing. SUPPORTS marker 047 (small-perturbation control vs. point-forcing).
- The key insight, formalized by Ott, Grebogi, and Yorke (1990) in their seminal work on controlling chaos, is that control becomes not a matter of forcing an impossible transition to any arbitrary state, but rather a strategic shift of the basins themselves—the regions of state-space that lead to each attractor—so that the system's natural dynamics carry it toward a desired outcome.
- Chaos
- the attractor can be a chaotic ecological regime, a chaotic cardiac rhythm, or a chaotic neural pattern. Economics and finance → the rule is a nonlinear macroeconomic or market model; the state space is the macroeconomic-variable or portfolio-state space; sensitive dependence (when present) appears at parameter regimes near bifurcations; the attractor is the irregular business-cycle or market regime. Engineering control → the rule is the controlled-system dynamics; the state space is the controllable-variable space; sensitive dependence is what the controller exploits (in chaos-based mixing or synchronization) or suppresses (in vibration control); the attractor is the operating envelope, possibly with embedded unstable periodic orbits exploitable for OGY-type control
This sourceOriginating treatment of the OGY method for stabilizing unstable periodic orbits embedded in a chaotic attractor using small targeted perturbations.
- the attractor can be a chaotic ecological regime, a chaotic cardiac rhythm, or a chaotic neural pattern. Economics and finance → the rule is a nonlinear macroeconomic or market model; the state space is the macroeconomic-variable or portfolio-state space; sensitive dependence (when present) appears at parameter regimes near bifurcations; the attractor is the irregular business-cycle or market regime. Engineering control → the rule is the controlled-system dynamics; the state space is the controllable-variable space; sensitive dependence is what the controller exploits (in chaos-based mixing or synchronization) or suppresses (in vibration control); the attractor is the operating envelope, possibly with embedded unstable periodic orbits exploitable for OGY-type control
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