Stabilizing near-nonhyperbolic chaotic systems and its potential applications in neuroscience
Debin Huang
Abstract
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 any 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 OGY-type methods will fail to stabilize. The technique is successfully used to the famous Hindmarsh-Rose model neuron and the Rossler hyperchaos system.
Create a lesson
Related papers
A comparison of three models of a whirling string as it becomes chaotic
Nicholas B. Tufillaro
Modal interactions in strongly nonlinear coupled oscillators with closely spaced modes and nonclassical damping distribution
C. A. Hubay, T. Kalmar-Nagy, L. Bergman et al.
Nonintegrability theorem on perturbed integrable Hamiltonian dynamical systems with two independent resonances
Nikos Zafeiriadis, Efthymia Meletlidou, Christos Efthymiopoulos et al.
PRISM: Unifying multiphysics optothermal transport and identifiability-guided inference for nanoscale thermal metrology
Yicong Qiu, Ziyang Zhong, Ziyan Qian et al.
Ultraslow diffusion emerging from local symmetry breaking in quenched disorder
Jin Liu, Rainer Klages, Huihai Wang et al.
A model for the dimension of the inertial manifold of the Kuramoto-Sivashinsky equation
Melisa Y. Vinograd, Patricio Clark di Leoni