Creation of Three‐Scroll Hidden Conservative Lorenz‐Like Chaotic Flows

Abstract

AbstractIn contrast to the various well‐known two‐scroll hidden Lorenz‐like attractors, little seems to be known about three‐scroll hidden conservative chaotic flows in the 3D Lorenz‐like system family whose Kaplan–Yorke dimension is approximately equal to . This technical note first proposes a three‐scroll chaotic system, i.e., , , , which generates three‐scroll hidden chaotic flows without equilibrium points when . Moreover, its Kaplan–Yorke dimension is . Then, for and , this system has another type of singularly degenerate heteroclinic cycle consisting of two different equilibria in the lines of semi‐hyperbolic equilibria and , i.e., and , with . With a small perturbation of , the kind of three‐scroll hidden conservative chaotic flows described above are created. Finally, five cycles are obtained when the proposed system undergoes Hopf bifurcation.