Generating one-, two-, three- and four-scroll attractors from a novel four-dimensional smooth autonomous chaotic system

A new four-dimensional quadratic smooth autonomous chaoticsystem is presented in this paper, which can exhibit periodic orbitand chaos under the conditions on the system parameters.Importantly, the system can generate one-, two-, three- andfour-scroll chaotic attractors with appropriate choices ofparameters. Interestingly, all the attractors are generated only bychanging a single parameter. The dynamic analysis approach in thepaper involves time series, phase portraits, Poincar'{e} maps,a bifurcation diagram, and Lyapunov exponents, to investigate somebasic dynamical behaviours of the proposed four-dimensional system.