### Abstract

Driving trajectories to a desirable attractor for dynamical systems with multiple coexisting attractors has been a challenging problem in the field of chaos control. We develop an algorithm to steer most trajectories to the desirable attractor by using only small feedback control. The idea is to build a hierarchy of paths to the desirable attractor and then stabilize trajectories around one of the paths in the hierarchy. A substantial improvement in the probability for a random trajectory to asymptote to the desirable attractor has been achieved when there are fractal basin boundaries in the phase space.

Original language | English |
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Pages (from-to) | 375-383 |

Number of pages | 9 |

Journal | Physics Letters A |

Volume | 221 |

Issue number | 6 |

Publication status | Published - 14 Oct 1996 |

### Keywords

- FRACTAL BASIN BOUNDARIES
- RIDDLED BASINS
- PROPORTIONAL FEEDBACK
- DYNAMICAL-SYSTEMS
- CHAOTIC SYSTEMS
- SYNCHRONIZATION
- INTERMITTENCY

### Cite this

*Physics Letters A*,

*221*(6), 375-383.

**Driving trajectories to a desirable attractor by using small control.** / Lai, Y C ; Lai, Ying-Cheng.

Research output: Contribution to journal › Article

*Physics Letters A*, vol. 221, no. 6, pp. 375-383.

}

TY - JOUR

T1 - Driving trajectories to a desirable attractor by using small control

AU - Lai, Y C

AU - Lai, Ying-Cheng

PY - 1996/10/14

Y1 - 1996/10/14

N2 - Driving trajectories to a desirable attractor for dynamical systems with multiple coexisting attractors has been a challenging problem in the field of chaos control. We develop an algorithm to steer most trajectories to the desirable attractor by using only small feedback control. The idea is to build a hierarchy of paths to the desirable attractor and then stabilize trajectories around one of the paths in the hierarchy. A substantial improvement in the probability for a random trajectory to asymptote to the desirable attractor has been achieved when there are fractal basin boundaries in the phase space.

AB - Driving trajectories to a desirable attractor for dynamical systems with multiple coexisting attractors has been a challenging problem in the field of chaos control. We develop an algorithm to steer most trajectories to the desirable attractor by using only small feedback control. The idea is to build a hierarchy of paths to the desirable attractor and then stabilize trajectories around one of the paths in the hierarchy. A substantial improvement in the probability for a random trajectory to asymptote to the desirable attractor has been achieved when there are fractal basin boundaries in the phase space.

KW - FRACTAL BASIN BOUNDARIES

KW - RIDDLED BASINS

KW - PROPORTIONAL FEEDBACK

KW - DYNAMICAL-SYSTEMS

KW - CHAOTIC SYSTEMS

KW - SYNCHRONIZATION

KW - INTERMITTENCY

M3 - Article

VL - 221

SP - 375

EP - 383

JO - Physics Letters A

JF - Physics Letters A

SN - 0375-9601

IS - 6

ER -