A new method for generating chaotic system with arbitrary shaped distributed attractors

In this paper, a new method for generating a chaotic system with arbitrary shaped (including heart-shaped, oval, circle, piecewise-linear, and cuboid) distributed attractors is proposed. In this article, a simple four-wing chaotic attractor is first presented by using a periodic piecewise function instead of a constant parameter in the Lorenz system, on the basis of which the chaotic system with arbitrary shaped distributed attractors in the plane can be constructed. This means that the distributed chaotic attractors can be arranged in an arbitrary shape in the plane. The chaotic system can generate any quantity of distributed chaotic attractors, and simulation results show that any desired number of positive Lyapunov exponents can be obtained. Therefore, the chaotic system will have more complicated dynamic characteristics. The dynamical mechanisms of this chaotic system are further investigated, and theoretical analysis and numerical simulation are in accordance with each other, which verifies the effectiveness of the approach. Lastly, the proposed chaotic system is used for image encryption. Numerical results show that the proposed scheme has an excellent performance.