Controlling Dynamics of Hidden Attractors
- 1 April 2015
- journal article
- Published by World Scientific Pub Co Pte Ltd in International Journal of Bifurcation and Chaos
- Vol. 25 (4)
- https://doi.org/10.1142/s0218127415500613
Abstract
Amplitude death (AD) in hidden attractors is attained with a scheme of linear augmentation. This linear control scheme is capable of stabilizing the system to a fixed point state even when the original system does not have any fixed point. Depending on the control parameter, different routes to AD such as boundary crises and Hopf bifurcation are observed. Lyapunov exponent and amplitude index are used to study the dynamical properties of the system.Keywords
This publication has 20 references indexed in Scilit:
- Complicated basins and the phenomenon of amplitude death in coupled hidden attractorsPhysics Letters A, 2014
- Oscillation quenching mechanisms: Amplitude vs. oscillation deathPhysics Reports, 2013
- Elementary quadratic chaotic flows with no equilibriaPhysics Letters A, 2013
- Amplitude death: The emergence of stationarity in coupled nonlinear systemsPhysics Reports, 2012
- Hidden attractor in smooth Chua systemsPhysica D: Nonlinear Phenomena, 2012
- Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua’s circuitsJournal of Computer and Systems Sciences International, 2011
- Algorithms for searching for hidden oscillations in the Aizerman and Kalman problemsDoklady Mathematics, 2011
- Localization of hidden Chuaʼs attractorsPhysics Letters A, 2011
- Algorithm for localizing Chua attractors based on the harmonic linearization methodDoklady Mathematics, 2010
- Amplitude death in coupled chaotic oscillatorsPhysical Review E, 2005