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Despite recent advances, existing models still face fundamental challenges in capturing complex temporal patterns, especially in scenarios involving non-linear dynamics, time-varying behaviours, and long-range dependencies. Recurrent Neural Networks and transformers are limited by their reliance on discrete updates and fixed positional encodings, while classical state-space models are constrained by static system parameters and linear assumptions. To address these limitations, we propose a Resilient State-Space Network, a unified framework that integrates zero-order hold discretization to maintain continuity in state evolution, complex-valued eigendecomposition to capture frequency-phase dynamics, and a dynamic parameter network based on the Kolmogorov-Arnold representation theorem, which generates time-varying gain matrices and adaptive sampling intervals\u2014thereby overcoming the linear time-invariant constraints of traditional State Space Models. Resilient State-Space Network is validated on three benchmark datasets: RAVDESS, SAVEE, and DISFA. The model is compared against strong baselines, including deep state space models, attention-based architectures, and temporal convolutional networks. Experimental results demonstrate that Resilient State-Space Network consistently outperforms existing methods, achieving accuracy improved from 89.5% to 90.8% on RAVDESS, 88.7% to 95.4% on SAVEE, and 79.1% to 80.8% on DISFA. Resilient State-Space Network establishes a unified modelling framework that combines physical modelling with deep learning. This approach introduces a new paradigm for time-series modelling and opens new directions for the design of physics-inspired neural networks, carrying significant theoretical implications and potential for practical applications. The code will be available at https:\/\/github.com\/SWU1111\/RSN.<\/jats:p>","DOI":"10.1093\/jcde\/qwaf092","type":"journal-article","created":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T20:08:00Z","timestamp":1758312480000},"page":"32-50","source":"Crossref","is-referenced-by-count":0,"title":["Resilient State-Space Network: A dynamically adaptive framework for non-linear modelling of temporal dependencies"],"prefix":"10.1093","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-0928-5602","authenticated-orcid":false,"given":"Chenyu","family":"Xue","sequence":"first","affiliation":[{"name":"College of Computer and Information Science, Southwest University , Tiansheng Road, Chongqing, 400715 ,","place":["China"]}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-2096-3172","authenticated-orcid":false,"given":"Ziqing","family":"Quan","sequence":"additional","affiliation":[{"name":"College of Computer and Information Science, Southwest University , Tiansheng Road, Chongqing, 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