Abstract
Robust chaos in the discrete system is suggested to have practical as well as theoretical importance since it can obtain reliable operation in the chaotic mode. However, it receives only moderate attention and only focuses on a finite chaotic parameter space and small Lyapunov exponents. This paper introduces a two-dimensional smooth map and studies its robustness of chaos in the infinite parameter space. Then, a compound operation-based optimization control method is introduced to increase the map complexity in the measure of Lyapunov exponent. The introduced method is simple and provides a new pathway for exploring the robustness and complexity of discrete chaotic system. Finally, we design a chaos-based pseudo-random number generator (CPNG) based on the optimized robust chaotic map, and the careful analysis shows that the proposed CPNG has high quality of randomness and has passed the rigorous National Institute of Standards and Technology (NIST) test.
Highlights
With the rapid development of network communication, the data security and encryption have been paid more and more attention by engineers and scientists [1], [2]
By exploring the relationship of system parameters and scale transformation of state variables, we find that the Lyapunov exponents of this discrete map remains invariable and the signal amplitudes change regularly following some functional relationship when some parameters vary in infinite real space
Aiming at the properties of limited chaotic parameter space and small Lyapunov exponent for the existing discrete maps, this paper introduced a two-dimensional smooth map and studied its dynamical behavior
Summary
With the rapid development of network communication, the data security and encryption have been paid more and more attention by engineers and scientists [1], [2]. System by combining different one-dimensional chaotic maps in a non-linear way, but the Lyapunov exponent of the system is small and the sequence complexity is not high To avoid this deficiency, Wang and Yuan [15], Zhou et al [16] and Yuan et al [17] introduced the cascading method for constructing discrete chaotic system, which can enlarge both the maximum Lyapunov exponent and the system parameter range of chaos. We have found that robust chaos exists in continuous chaotic systems with infinite parameter space These parameters can regularly control the amplitude of system signal, and the Lyapunov exponent remains invariable [34]–[36]. When b >1, we have |λ1| < 1 and |λ2| > 1, fixed point P0 is an unstable saddle point
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