Generating digital chaotic systems of the simplest structure via a strongly connected graph inverse approach

Qianxue Wang, Dongsheng Kuang and Simin Yu

Chaos, Solitons & Fractals, 2024, vol. 189, issue P1

Abstract: This paper designs the simplest m-dimensional (m=2,3,4,…) digital chaotic system using a strongly connected graph inverse approach. Compared to previous systems, this approach significantly simplifies the system structure while enhancing statistical performance. First, in the m-dimensional digital iterative system, we construct 2m-state transition graph with bidirectional direct paths between any two states. Under the condition that the bitwise XOR result between any two states equals the combination of the current m unilateral infinite sequence outputs, we derive the corresponding simplest uncoupled m-dimensional iterative functions based on the inverse approach. Second, based on the simplest uncoupled m-dimensional iterative functions, we develop a cascaded closed-loop coupling approach to obtain the corresponding simplest fully coupled m-dimensional iterative functions, theoretically proving that they satisfy Devaney’s chaos definition. Compared to previous systems, this closed-loop coupling method not only simplifies the system structure, making it the simplest form among all fully coupled m-dimensional iterative functions, but also significantly improves statistical performance, as evidenced by passing both NIST and TestU01 tests. Finally, we validate the effectiveness and superiority of the simplest m-dimensional digital chaotic system through circuit design and FPGA simulation experiments.

Keywords: Digital chaotic systems; Strongly connected graph inverse approach; Cascaded closed-loop coupling; Devaney’s chaos definition; FPGA simulation (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:189:y:2024:i:p1:s0960077924012074

DOI: 10.1016/j.chaos.2024.115655

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