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Entropy 2019, 21(1), 34; https://doi.org/10.3390/e21010034

Dynamics and Complexity of a New 4D Chaotic Laser System

1
Institute for Mathematical Research, Universiti Putra Malaysia, UPM Serdang 43000, Malaysia
2
The Branch of Applied Mathematics, Applied Science Department, University of Technology, Baghdad 10075, Iraq
3
Malaysia-Italy Centre of Excellence for Mathematical Science, Universiti Putra Malaysia, UPM Serdang 43000, Malaysia
4
Department of Mathematics, Universiti Putra Malaysia, UPM Serdang 43000, Malaysia
*
Author to whom correspondence should be addressed.
Received: 11 December 2018 / Revised: 26 December 2018 / Accepted: 2 January 2019 / Published: 7 January 2019
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Abstract

Derived from Lorenz-Haken equations, this paper presents a new 4D chaotic laser system with three equilibria and only two quadratic nonlinearities. Dynamics analysis, including stability of symmetric equilibria and the existence of coexisting multiple Hopf bifurcations on these equilibria, are investigated, and the complex coexisting behaviors of two and three attractors of stable point and chaotic are numerically revealed. Moreover, a conducted research on the complexity of the laser system reveals that the complexity of the system time series can locate and determine the parameters and initial values that show coexisting attractors. To investigate how much a chaotic system with multistability behavior is suitable for cryptographic applications, we generate a pseudo-random number generator (PRNG) based on the complexity results of the laser system. The randomness test results show that the generated PRNG from the multistability regions fail to pass most of the statistical tests. View Full-Text
Keywords: Hopf bifurcation; self-excited attractors; multistability; sample entropy; PRNG Hopf bifurcation; self-excited attractors; multistability; sample entropy; PRNG
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Natiq, H.; Said, M.R.M.; Al-Saidi, N.M.G.; Kilicman, A. Dynamics and Complexity of a New 4D Chaotic Laser System. Entropy 2019, 21, 34.

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