Behavioral study of a new chaotic system

A new three-dimensional continuous autonomous system is proposed in this paper and it exhibits single scroll chaotic behavior in a particular parameter region. By linear stability analysis and numerical simulations, we investigate different dynamical observations with respect to system parameters and try to understand the route to generation of chaos. For a large portion of the parameter region, we see a sudden birth of a period-three limit cycle. Then the period-three orbit turns into a chaotic state through typical Pomeau-Manneville intermittent route to chaos. Lyapunov exponent and Kaplan-Yorke dimension are used to verify the chaotic behavior. It becomes periodic via inverse period-doubling route for higher values of the parameters. A two-parameter bifurcation diagram is shown which distinguishes the chaotic region from other periodic and steady-state regions.