Multistability in a 3D Circulant Chaotic Flow: the Circulant Symmetry of Coexisting Dynamics

In this paper, a novel chaotic flow exhibiting circulant symmetry is modeled and analyzed. The chaotic flow’s dynamical behavior is thoroughly investigated, revealing that it is dissipative over the studied parameter values. A basic equilibrium analysis shows that four of the system’s equilibrium points are stable. Notably, the system exhibits two distinct sets of three coexisting chaotic attractors, each set displaying circulant symmetry. To the best of our knowledge, such a system has not been previously reported in the literature. Bifurcation analysis with respect to all three system parameters confirms the rich dynamical behavior, supported by corresponding Lyapunov exponent spectra. The basins of attraction reveal rare V-shaped boundaries, adding to the system’s uniqueness. Furthermore, the circulant symmetry is clearly reflected in the basins of attraction of the coexisting attractors.