Modified jerk system with self-exciting and hidden flows and the effect of time delays on existence of multi-stability

In this paper, we report a new chaotic jerk system which shows self-excited and hidden oscillations depending on its parameters. Dynamic analysis shows that the proposed system exhibits multi-stability and coexisting attractors. To study the effect of time delays on the multi-stability feature of the system, we introduce multiple time delays in the third state variable. Investigation of dynamical properties of the time-delayed system shows the disappearance of multi-stability. Such a feature has not been reported earlier in the literatures.