A new chaotic system with different equilibria and attractors

This paper presents an interesting four-dimensional chaotic system with different equilibria and attractors. The proposed system has three quadratic nonlinearities and has no equilibrium, three equilibria and infinite equilibria for different regions of system parameters. As the values of parameters change, the system performs stable, periodic and chaotic states. Also it has period-doubling bifurcation which leads to chaos and has Hopf bifurcation which makes the system loses stability. Moreover, the system generates hidden chaotic attractor when it has no equilibria and generates coexisting chaotic attractors for different initial values. The electronic circuit implementation of the system is given to illustrate the corresponding dynamical properties of the system.