Two-Dimensional Modular Chaotification System for Improving Chaos Complexity

Chaotic systems are widely studied in various research areas such as signal processing and secure communication. Existing chaotic systems may have drawbacks such as discontinuous chaotic ranges and incomplete output distributions. These drawbacks may lead to the defects of some chaos-based applications. To accommodate these challenges, this paper proposes a two-dimensional (2D) modular chaotification system (2D-MCS) to improve the chaos complexity of any 2D chaotic map. Because the modular operation is a bounded transform, the improved chaotic maps by 2D-MCS can generate chaotic behaviors in wide parameter ranges while existing chaotic maps cannot. Three improved chaotic maps are presented as typical examples to verify the effectiveness of 2D-MCS. The chaos properties of one example of 2D-MCS are mathematically analyzed using the definition of Lyapunov exponent. Performance evaluations demonstrate that these improved chaotic maps have continuous and large chaotic ranges, and their outputs are distributed more uniformly than the outputs of existing 2D chaotic maps. To show the application of 2D-MCS, we apply the improved chaotic maps of 2D-MCS to secure communication. The simulation results show that these improved chaotic maps exhibit better performance than several existing and newly developed chaotic maps in terms of resisting different channel noise.