Abstract
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.
Highlights
C HAOIC system has received a lot of attentions on account of its bright application prospects in the field of nonlinear engineering [1]-[6]
The original chaotic system of infinitely many equilibrium points or switchable equilibrium point has the ability to generate infinitely many coexisting attractors [9], [10]. Another better method for constructing the system with extremely multistability was found, the initial-offset boosted attractors of infinitely many coexistence can be obtained by introducing the trigonometric functions to some specific linear terms of chaotic system [11]-[13]
We focus on a new chaotic system of extremely multistability which can generate infinitely many coexisting attractors
Summary
C HAOIC system has received a lot of attentions on account of its bright application prospects in the field of nonlinear engineering [1]-[6]. This paper successfully constructed a new 3D chaotic system which can produce infinitely many coexisting attractors by using the boosted control of cosine function. Due to the introduction of two cosine functions, it can generate two directions infinitely many coexisting attractors by changing different initial conditions. We focus on a new chaotic system of extremely multistability which can generate infinitely many coexisting attractors. Reconstructing the system equation by introducing two boosted control of cosine function for state variables x, z, the chaotic system can generate infinitely many coexisting attractors of two directions on the phase plane. It indicates the running track of the system will compress to an empty set, and the progressive motion will tends to be stable in a domain of attraction
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