1-D Complex-Variable Chaotic Model With Hardware Implementation

Discrete chaotic maps in the real number field have been widely investigated and applied to various applications. However, there has been limited focus on constructing discrete chaotic maps with complicated dynamics in the complex field. In light of this, this article proposes a 1-D complex-variable chaotic model (1-D-CCM), which can produce a multitude of 1-D complex-variable chaotic maps by combining unbounded analytic functions and locally bounded analytic functions. To illustrate the effectiveness of 1-D-CCM, we construct two 1-D complex-variable chaotic maps by combining inverse trigonometric functions and hyperbolic trigonometric functions. We provide theoretical proof of a new 1-D complex-variable chaotic map as one example to demonstrate that the generated chaotic maps satisfy the chaos definition in terms of Lyapunov exponent. Property analysis reveals distinct strange attractors and hyperchaotic behaviors for the two 1-D complex-variable chaotic maps. Performance evaluations show that the example maps of 1-D-CCM model can achieve a 0–1 test value of 1.0017, a C₀ complexity of 0.7253, a correlation dimension of 2.0242, and a sample entropy of 0.8288. Experimental results demonstrate superior performance indicators compared to other representative chaotic maps. We construct a hardware platform using a microcontroller to implement the attractors of the two new complex-variable chaotic maps. Finally, we design pseudorandom number generators to demonstrate the potential applications of the two 1-D complex-variable chaotic maps.