Dynamics and Complexity of a New 4D Chaotic Laser System

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.

Pseudo-Random Number Generator Based on Logistic Chaotic System

“…The extraction method in Table 3 represents the number in the 15-digit numerical sequence. (5,6,7,8) 10.4220 10.4218 10.4223 10.4222 (9,10,11,12) 10.4220 10.4224 10.4218 10.4220 (1,5,9,13) 10.4221 10.4220 10.4219 10.4223 (2,6,10,14) 10.4222 10.4221 10.4221 10.4221 (3,7,11,15) 10.4223 10.4214 10.4222 10.4219 Table 3 shows the proposed method has little effect on the randomness. In this paper, the last three extraction methods in Table 3 are selected to extract the initial value, system initial value and iteration times of the next chaotic system.…”

“…There is an interesting relationship between chaos and cryptography. According to this relationship, many characteristics of chaotic systems such as the sensitivity of initial value/system parameters, ergodicity, deterministic dynamics, and structural complexity are considered to be the diffusion and confusion of keys [3][4][5][6]. Compared with traditional encryption systems, they have certain randomness [7,8].…”

Dynamical Complexity and Multistability in a Novel Lunar Wake Plasma System

“…is nonlinear behavior is termed as coexisting attractors or multistability. Multistability behaviors [11,12] of the physical system act as important feature in the dynamics of nonlinear systems. Experimentally, multistability feature was firstly investigated in a Q-switched gas laser [13]; thereafter, various works [14,15] were reported in different complex systems exhibiting multistability features.…”

Entropy Analysis and Image Encryption Application Based on a New Chaotic System Crossing a Cylinder

“…Chaotic systems with stable equilibria [ 8 ], chaotic flows with no equilibria [ 9 , 10 ], and chaotic flow with circular equilibria [ 11 , 12 ] are some of such counterexamples. Investigating new chaotic flows has been done in the literature [ 13 ]. Many chaotic flows with various features are being proposed every year [ 14 , 15 , 16 ].…”