Eur. Phys. J. Special Topics 229, 1319-1333 (2020)
https://doi.org/10.1140/epjst/e2020-900134-4

Regular Article

Infinity dynamics and DDF control for a chaotic system with one stable equilibrium

¹ School of Civil Engineering and Architecture, Xi’an University of Technology, Xi’an 710048, P.R. China
² Shaanxi Engineering Research Center of Controllable Neutron Source, School of Science, Xijing University, Xi’an 710123, P.R. China
³ School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, P.R. China

^a e-mail: williamchristian@163.com

Received: 12 July 2019
Received in final form: 9 September 2019
Published online: 26 March 2020

Abstract

Hidden attractors in chaotic dynamical systems can be found by exploring the basin of attraction which has no intersect with any equilibria. Controlling chaos in these systems are complicated, which needs developed methods. In this paper, a 3D jerk system with only one stable equilibrium and hidden attractor is analyzed in infinity by the help of the Poincare compactification in R³. Meanwhile, a distributed delayed feedback (DDF) control scheme for this system is proposed. By using the center manifold theory of functional differential equation (FDE), Hopf bifurcation for the DDF control system is analyzed and obtained. Results confirm the accuracy of the bifurcation analysis and the effectiveness of the proposed DDF control strategy.