A New Three-dimensional Chaotic System without Equilibrium Points, Its Dynamical Analyses and Electronic Circuit Application

Original scientific paper In this paper, a new three-dimensional chaotic system without equilibrium points is introduced and analysed. Basic dynamical analysis of this new chaotic system without equilibrium points is carried out by means of system equilibria, phase portraits, sensitivity to initial conditions, fractal dimension and chaotic behaviours. In addition, in this paper Lyapunov exponents spectrum and bifurcation analysis of the proposed chaotic system have been executed by means of selected parameters. The chaotic system without equilibrium points has been executed by detailed theoretical analysis as well as simulations with designed electronical circuit. A chaotic system without equilibrium points is also known as chaotic system with hidden attractor and there are very few researches in the literature. Since they cannot have homoclinic and heteroclinic orbits, Shilnikov method cannot be applied to find whether the system is chaotic or not. Therefore, it can be useful in many engineering applications, especially in chaos based cryptology and coding information. Furthermore, introduced chaotic system without equilibrium points in this paper can have many unknown dynamical behaviours. These behaviours of the strange chaotic attractors deserve further investigation.