https://doi.org/10.1140/epjp/i2017-11665-7
Regular Article
Control of chaos: Lie algebraic exact linearization approach for the Lü system
Department of Applied Mathematics & Statistics, Institute of Space Technology, 44000, Islamabad, Pakistan
* e-mail: m_anam20@yahoo.com
Received:
23
June
2017
Accepted:
22
August
2017
Published online:
18
October
2017
In this article, nonlinear control of the Lü chaos is presented by transforming a Lü system in a linear controllable system by using the Lie algebraic exact linearization method. Numerically, control of chaos does not have much place in current literature unless one actually finds and displays the controller in the chaotic system. The controller for the Lü system is designed for an arbitrary output. Based on this controller, both linear and nonlinear outputs are discussed in detail. Numerical simulations are carried out for all necessary aspects of the Lü problem that justify our analytical findings. Moreover, the stabilization of the Lü system based on the linear controllable system is discussed in the form of limit cycles and Hopf bifurcation. In particular, the numerical Hopf bifurcation diagram is presented using the numerical continuation technique.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, 2017
