Dynamics and Optimization Control of a Robust Chaotic Map

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.

Keywords

• Discrete map
• dynamics
• parameter space
• Lyapunov exponent