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Entropy 2018, 20(1), 12; https://doi.org/10.3390/e20010012

A New Chaotic System with Multiple Attractors: Dynamic Analysis, Circuit Realization and S-Box Design

1
School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang 330013, China
2
Department of Electrical and Electronics Engineering, Faculty of Technology, Sakarya University, Serdivan 54187, Turkey
3
School of Electronic and Information Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China
4
School of Electrical and Electronic Engineering, Hubei University of Technology, Wuhan 430068, China
5
Department of Computer Engineering, Faculty of Computer and Information Sciences, Sakarya University, Serdivan 54187, Turkey
*
Author to whom correspondence should be addressed.
Received: 17 November 2017 / Revised: 22 December 2017 / Accepted: 25 December 2017 / Published: 27 December 2017
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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. View Full-Text
Keywords: new chaotic system; multiple attractors; electronic circuit realization; S-Box algorithm new chaotic system; multiple attractors; electronic circuit realization; S-Box algorithm
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Lai, Q.; Akgul, A.; Li, C.; Xu, G.; Çavuşoğlu, Ü. A New Chaotic System with Multiple Attractors: Dynamic Analysis, Circuit Realization and S-Box Design. Entropy 2018, 20, 12.

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