A chaotic system with rounded square equilibrium and with no-equilibrium

Chaotic systems with an infinite number of equilibrium points and chaotic ones without equilibrium have received a significant attention in the last years because they belong to a class of systems with “hidden attractor”. In this work, we introduce a three-dimensional chaotic system displaying both hidden attractors with infinite equilibria and hidden attractors without equilibrium. Surprisingly, when the system exhibits hidden attractors with infinite equilibria, it has a rounded square curve of equilibrium points. Dynamical properties of the new system are analyzed through equilibrium points, phase portraits, bifurcation diagram, and maximal Lyapunov exponents. Furthermore, circuit implementation of the system is presented showing another approach to study such system as well as its feasibility.