The analysis of complex behaviours of a novel three dimensional autonomous system

This paper introduces a new three dimensional autonomous system with five equilibrium points. It demonstrates complex chaotic behaviours within a wide range of parameters, which are described by phase portraits, Lyapunov exponents, frequency spectrum, etc. Analysis of the bifurcation and Poincaré map is used to reveal mechanisms of generating these complicated phenomena. The corresponding electronic circuits are designed, exhibiting experimental chaotic attractors in accord with numerical simulations. Since frequency spectrum analysis shows a broad frequency bandwidth, this system has perspective of potential applications in such engineering fields as secure communication.