Eur. Phys. J. Spec. Top. (2022) 231: 2455-2466
https://doi.org/10.1140/epjs/s11734-022-00553-2

Regular Article

Dynamical analysis and fixed-time synchronization of a chaotic system with hidden attractor and a line equilibrium

¹ Shaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source School of Science, Xijing University, 710123, Xi’an, People’s Republic of China
² Xi’an Key Laboratory of Advanced Photo-electronics Materials and Energy Conversion Device School of Science, Xijing University, 710123, Xi’an, People’s Republic of China

^b williamchristian@163.com

Received: 3 November 2021
Accepted: 30 March 2022
Published online: 17 April 2022

Abstract

To further understand the dynamic behaviors of chaotic systems with hidden attractor and a line equilibrium, we analyzed the fundamental dynamics of the system, including the attractor types, Lyapunov exponents, and Poincaré section of the system under different parameters. Moreover, the infinity dynamics of the system is studied based on Poincaré compactification theory, and give the complete description of the phase portrait of the system at infinity. Furthermore, the fixed-time synchronization observer of system is proposed based on the fixed-time stability theory, which guarantees the synchronization of the master–slave system in settling time. Finally, the simulation is given to illustrate the effectiveness and validity of the theoretical results.