A new megastable chaotic oscillator with singularity

While multistability is known as a hot topic in nonlinear dynamics, two exceptional cases of multistable systems have been investigated less: extreme multistable systems and megastable systems are two newer categories of multistable dynamical systems. In this paper, for the first time, a chaotic megastable oscillator is introduced which has a singularity in its equations. The effect of the amplitude and frequency of forcing term on the dynamical behavior of the designed system is investigated. With the help of the bifurcation diagram and the Lyapunov exponents’ diagram, it is shown that the proposed oscillator can show a variety of dynamical behaviors, including limit cycle, torus, and strange attractor.