Dynamic analysis and synchronisation control of a novel chaotic system with coexisting attractors

In this paper, a novel four-dimensional continuous chaotic system is constructed from the simplified Lorenz-like system. The novel system has three equilibria, strange attractors, coexisting attractors, and performs Hopf bifurcation with the variation of system parameters. The coexisting attractors, which are the most remarkable dynamic features of the system, are numerically studied. The coexisting attractors show that the system coexists as a pair of point, periodic, and chaotic attractors. Some basic dynamic behaviours are studied as well. The synchronisation control problem of the system is analysed. The theoretical and numerical analyses demonstrate that the system can easily achieve synchronisation by using the passive control technique.