A Novel Circulant System with Six Coexisting Symmetric Conservative Chaotic Seas

This study presents a new three-dimensional circulant chaotic system with both conservative and dissipative dynamics. It is characterized by six coexisting symmetric seas. The system’s governing equations exhibit circulant symmetry, ensuring invariance under cyclic permutations of variables, and incorporate cubic nonlinearities that give rise to complex dynamics. Through a detailed analysis, we demonstrate the system’s rich behavior, including equilibrium points, bifurcations, Lyapunov exponent spectra, and the region occupied by the chaotic sea structures. The dynamics are distinct in their regions of initial conditions, highlighting the multistability. Bifurcation analysis reveals transitions between chaotic, periodic, dissipative, and conservative regimes, while Lyapunov exponents confirm the existence of conservative and dissipative dynamics. The extent of the chaotic seas exhibits sharp boundaries of chaotic dynamics which are discussed mathematically. Also, it shows embedded quasi-periodic invariant tori, further enriching the system’s complexity. This work advances the understanding of symmetric chaotic systems.