A Novel Hyperchaotic System Derived from Asymmetric Bidirectional Coupling of Two Lorenz Oscillators: Synchronization Analysis and Cryptographic Applications
Abstract
This paper investigates a six-dimensional coupled Lorenz system obtained through bidirectional asymmetric diffusive coupling of two identical Lorenz oscillators. The proposed model is analyzed from both dynamical and synchronization perspectives. Dissipativity conditions, equilibrium points, local stability properties, and Lyapunov spectra are systematically examined. The results reveal wide regions of chaotic and hyperchaotic behavior, with up to three positive Lyapunov exponents depending on the coupling parameters. These findings provide a practical framework for selecting coupling configurations that guarantee hyperchaotic dynamics while preserving the simplicity of the classical Lorenz structure. \\ A Lyapunov-based synchronization analysis is then developed. By exploiting effective attractor bounds obtained from the actual system trajectories rather than conservative worst-case estimates, a less restrictive sufficient synchronization condition is derived. Under the classical Lorenz parameters, synchronization is guaranteed for α1+α2>15.1. \\ The synchronization performance is further evaluated through a parametric analysis of the synchronization time. Numerical results show that increasing the coupling strength significantly accelerates convergence toward the synchronization manifold. For a broad range of admissible coupling values, synchronization times below $0.5$ second are achieved, whereas previously reported Lorenz-based synchronization schemes typically require approximately $5$ seconds.
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BibTeX
@misc{hamdi2026novel,
title = {{A Novel Hyperchaotic System Derived from Asymmetric Bidirectional Coupling of Two Lorenz Oscillators: Synchronization Analysis and Cryptographic Applications}},
author = {Mimoun Hamdi and Mohamed Karim Hamdani and Kamel Abboudi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23276},
eprint = {2609.23276},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23276},
note = {CC0},
}
RIS
TY - UNPB
TI - A Novel Hyperchaotic System Derived from Asymmetric Bidirectional Coupling of Two Lorenz Oscillators: Synchronization Analysis and Cryptographic Applications
AU - Mimoun Hamdi
AU - Mohamed Karim Hamdani
AU - Kamel Abboudi
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23276
UR - https://arxiv.org/abs/2609.23276
AB - This paper investigates a six-dimensional coupled Lorenz system obtained through bidirectional asymmetric diffusive coupling of two identical Lorenz oscillators. The proposed model is analyzed from both dynamical and synchronization perspectives. Dissipativity conditions, equilibrium points, local stability properties, and Lyapunov spectra are systematically examined. The results reveal wide regions of chaotic and hyperchaotic behavior, with up to three positive Lyapunov exponents depending on the coupling parameters. These findings provide a practical framework for selecting coupling configurations that guarantee hyperchaotic dynamics while preserving the simplicity of the classical Lorenz structure. \\ A Lyapunov-based synchronization analysis is then developed. By exploiting effective attractor bounds obtained from the actual system trajectories rather than conservative worst-case estimates, a less restrictive sufficient synchronization condition is derived. Under the classical Lorenz parameters, synchronization is guaranteed for α_1+α_2>15.1. \\ The synchronization performance is further evaluated through a parametric analysis of the synchronization time. Numerical results show that increasing the coupling strength significantly accelerates convergence toward the synchronization manifold. For a broad range of admissible coupling values, synchronization times below $0.5$ second are achieved, whereas previously reported Lorenz-based synchronization schemes typically require approximately $5$ seconds.
ER -