Generating Infinitely Many Coexisting Attractors via a New 3D Cosine System and Its Application in Image Encryption

In this paper, a new third-order chaotic system which has extremely multistability is constructed by introducing the boosted control of cosine function. In comparison with other chaotic systems of extremely multistability, the proposed chaotic system can spontaneously generate the infinitely many coexisting attractors towards two directions of the phase plane. It indicates the proposed system can output more chaotic sequences of different amplitudes at the same time. This peculiar physical phenomena is very interesting and worth studying. Relative to original chaotic system, the chaos characteristic of the proposed system is obviously enhanced, the value of max Lyapunov exponent is increased significantly and the complexity value was higher. In particular, many periodic windows of the original chaotic system become chaos. It means the proposed chaotic system has better chaotic characteristics. If the new system is applied to the field of cryptography, it would be a better system model as a pseudo-random signal generator (PRSG). Then, the new image encryption algorithm is designed based on the proposed discrete system, and its safety performance is tested. The experimental results demonstrate the feasibility of its application in the field of cryptography.