A New Hyperchaotic Map and Its Manifold of Conditional Symmetry

Hu, Zhenxin; Li, Chunbiao; Qi, Xiaolong; Antoniades, Ioannis P.; Volos, Christos

doi:10.3390/sym18020212

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A New Hyperchaotic Map and Its Manifold of Conditional Symmetry

by

Zhenxin Hu

¹,

Chunbiao Li

^2,*

,

Xiaolong Qi

³,

Ioannis P. Antoniades

⁴

and

Christos Volos

⁴

¹

School of Electronic and Information Engineering, Nanjing University of Information Science & Technology, Nanjing 210044, China

²

School of Artificial Intelligence, Nanjing University of Information Science &Technology, Nanjing 210044, China

³

School of Network Security and Information Technology, Yili Normal University, Yining 835000, China

⁴

Laboratory of Nonlinear Systems, Circuits and Complexity, Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece

^*

Author to whom correspondence should be addressed.

Symmetry 2026, 18(2), 212; https://doi.org/10.3390/sym18020212

Submission received: 18 December 2025 / Revised: 16 January 2026 / Accepted: 21 January 2026 / Published: 23 January 2026

(This article belongs to the Section Engineering and Materials)

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Abstract

In this work, the polarity balance of a novel two-dimensional hyperchaotic map is considered, and thus the corresponding manifold of conditional symmetry is coined. The unique map has a simple structure but provides direct 2-D offset boosting, which brings the possibility for the construction of conditional symmetry by introducing an absolute value function. The corresponding evolution of the discrete sequences from the system is verified by the circuit implementation based on the microcontroller of CH32V307. The pseudorandom data from the map increases its adaptability for applications in information security. The hyperchaotic sequence-injected Ant Colony Optimization (ACO), Grey Wolf Optimizer (GWO), and Sparrow Search Algorithm (SSA) show their improved performance in the optimization algorithm. Robot path planning experiments confirm that all three algorithms exhibit superior convergence performance, global search capability, and path smoothness compared with the original algorithms.

Keywords: hyperchaotic map; 2-D offset boosting; conditional symmetry; path optimization

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MDPI and ACS Style

Hu, Z.; Li, C.; Qi, X.; Antoniades, I.P.; Volos, C. A New Hyperchaotic Map and Its Manifold of Conditional Symmetry. Symmetry 2026, 18, 212. https://doi.org/10.3390/sym18020212

AMA Style

Hu Z, Li C, Qi X, Antoniades IP, Volos C. A New Hyperchaotic Map and Its Manifold of Conditional Symmetry. Symmetry. 2026; 18(2):212. https://doi.org/10.3390/sym18020212

Chicago/Turabian Style

Hu, Zhenxin, Chunbiao Li, Xiaolong Qi, Ioannis P. Antoniades, and Christos Volos. 2026. "A New Hyperchaotic Map and Its Manifold of Conditional Symmetry" Symmetry 18, no. 2: 212. https://doi.org/10.3390/sym18020212

APA Style

Hu, Z., Li, C., Qi, X., Antoniades, I. P., & Volos, C. (2026). A New Hyperchaotic Map and Its Manifold of Conditional Symmetry. Symmetry, 18(2), 212. https://doi.org/10.3390/sym18020212

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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A New Hyperchaotic Map and Its Manifold of Conditional Symmetry

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