A novel parameter-controlled multiscroll memristive chaotic system with application to design five-element finite field encryption algorithm

Zeng-Jun Xin, Qiang Lai and Yuanmao Zhong

Chaos, Solitons & Fractals, 2026, vol. 210, issue P1

Abstract: This paper presents a unique memristive chaotic system, incorporating a non-ideal memristor. The internal state of this memristor is determined by a novel symmetrical three-segment piecewise-linear saturation function nested within a sine function which makes the system capable of multiscroll and multistability. The stability of equilibria and intricate dynamics within it are examined. The results show that by varying the parameters, this system can generate arbitrary numbers of multiscroll attractors, and there exist parameter-relied and initial-relied offset boosting phenomena, as well as parameter-relied symmetry. An encryption algorithm for mapping pixel values to a five-element finite field (GF(5)) is innovatively proposed, and its nonlinear transformation rules are derived from a carefully constructed 3-bit encoded permutation group. This design provides a structured yet highly nonlinear foundation for chaotic-based encryption applications.

Keywords: Chaos; Multiscroll attractor; Memristive chaotic system; Offset boosting; Image encryption (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:210:y:2026:i:p1:s0960077926007277

DOI: 10.1016/j.chaos.2026.118586

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