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An n-Dimensional Chaotic System Generation Method Using Parametric Pascal Matrix
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DOI：10.1109/TII.2022.3151984.png)
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Abstract
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When high-dimensional chaotic systems are applied to many practical applications, they are required to have robust and complex hyperchaotic behaviors. In this article, we propose a novel nD chaotic system construction method using the Pascal-matrix theory. First, a parametric Pascal matrix is constructed. Then, an nD chaotic system can be generated by using the parametric Pascal matrix as the parameter matrix of the system. Theoretical analysis shows that the generated nD chaotic systems have robust and complex chaotic behaviors, and they become nD Arnold Cat maps by fixing the parameters as some special values. Performance evaluations demonstrate that the nD chaotic systems have more complex chaotic behaviors and better distribution of outputs compared with existing HD chaotic systems. A 4-D Arnold Cat map and a 4-D chaotic map with hyperchaotic behaviors are generated as two examples. The two chaotic maps are then simulated on a microcontroller-based hardware platform and the chaotic sequences are tested to show good randomness.
Keywords:
Arnold cat map
chaos complexity
chaotic system
hardware implementation
hyperchaotic sequence
nonlinear system
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