Abstract
This paper reports about a novel three-dimensional chaotic system with three nonlinearities. The system has one stable equilibrium, two stable equilibria and one saddle node, two saddle foci and one saddle node for different parameters. One salient feature of this novel system is its multiple attractors caused by different initial values. With the change of parameters, the system experiences mono-stability, bi-stability, mono-periodicity, bi-periodicity, one strange attractor, and two coexisting strange attractors. The complex dynamic behaviors of the system are revealed by analyzing the corresponding equilibria and using the numerical simulation method. In addition, an electronic circuit is given for implementing the chaotic attractors of the system. Using the new chaotic system, an S-Box is developed for cryptographic operations. Moreover, we test the performance of this produced S-Box and compare it to the existing S-Box studies.
Highlights
The discovery of the well-known Lorenz attractor [1] in 1963 opened the upsurge of chaos research.In the decades thereafter, a large number of meaningful achievements on chaos control, chaotification, synchronization and chaos application have emerged continuously
We mainly focus on these tests: nonlinearity, outputs’ bit independence criterion (BIC), strict avalanche criterion (SAC), and differential approach probability (DP)
A special chaotic system with multiple attractors was studied in this letter
Summary
The discovery of the well-known Lorenz attractor [1] in 1963 opened the upsurge of chaos research. With the further research of chaos, scientists found that some nonlinear dynamic systems have a chaotic attractor and coexist with multiple attractors for a set of fixed parameter values. The investigation of chaos and multiple coexisting attractors is a very interesting research issue in academia. It helps to recognize the dynamic evolution of the actual system and promote the study of complexity science. The electronic circuit has become an important tool for the analysis of chaotic systems [27,28,29,30] This present paper considers a special polynomial chaotic system with the following features:. S-Box according to the system, and Section 7 summarizes the conclusions of this paper
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