Complexity-state characterization of nonlinear underwater acoustic dynamics via Adaptive Lempel–Ziv Networks

Short, noisy, and non-stationary underwater acoustic signals often contain local dynamical variations that are difficult to characterize from finite observations. This paper proposes the Adaptive Lempel–Ziv Network (ALZN), an interpretable transition-network framework that maps reconstructed local trajectory segments into complexity states defined by Lempel–Ziv parsing counts. Instead of describing a signal only through global amplitude partitions or ordinal ranks, ALZN uses an adaptive quantile-based symbolic mapping to capture local pattern-generation behavior and then records the temporal transitions among empirical irregularity levels. The resulting complexity-state graph is summarized by a compact five-dimensional network descriptor, covering node occupancy, transition uncertainty, edge density, weighted clustering, and global efficiency. Experiments on noisy chaotic systems show that ALZN can distinguish different nonlinear regimes and retain stable feature separability under noise contamination. Real-world underwater acoustic recognition experiments further demonstrate that the proposed descriptor retains vessel-related dynamical information while maintaining a low-dimensional and physically interpretable structure. These results indicate that ALZN provides a practical network-based tool for complexity-state characterization of short and noisy acoustic time series.