Stabilizing near-nonhyperbolic chaotic systems with applications

作者:Huang DB*
来源:Physical Review Letters, 2004, 93(21): 214101.
DOI:10.1103/PhysRevLett.93.214101

摘要

Based on the invariance principle of differential equations a simple, systematic, and rigorous feedback scheme with the variable feedback strength is proposed to stabilize nonlinearly finite-dimensional chaotic systems without any prior analytical knowledge of the systems. Especially the method may be used to control near-nonhyperbolic chaotic systems, which, although arising naturally from models in astrophysics to those for neurobiology, all Ott-Grebogi-York type methods will fail to stabilize. The technique is successfully used for the famous Hindmarsh-Rose neuron model, the FitzHugh-Rinzel neuron model, and the Rossler hyperchaos system, respectively.