Approximation identification for the stochastic time-delayed dynamical system

Ping Han, Qin Guo, Hongxia Zhang and Liang Wang

Physica A: Statistical Mechanics and its Applications, 2024, vol. 654, issue C

Abstract: This paper addresses the challenges of analyzing stochastic dynamical systems with a single time-delay within a data-driven framework. The presence of time-delay introduces non-Markovian characteristics to the system, complicating the analysis of its dynamic behavior using traditional approaches. Drawing inspiration from the small delay approximation, we apply a sparse identification technique to approximate the non-Markovian process with a Markovian one. This innovative method circumvents limitations associated with the system's dimensionality and the complexity of delayed diffusion terms, offering a versatile tool for investigating the dynamics of stochastic time-delayed systems. Our approach begins by establishing a connection between the system's coefficients and simulated data using the Kramers-Moyal formula, which captures the essential statistical properties of the system. We then leverage sparse identification to extract a concise model of the stochastic dynamical system, effectively eliminating the time-delay from consideration. The practicality and efficacy of our method are substantiated through a series of illustrative examples that showcase its application and validate its performance. By introducing this method, we aim to provide a novel analytical framework for stochastic time-delayed systems, advancing the current capabilities for modeling and understanding such complex dynamics.

Keywords: Stochastic dynamical system; Time-delay; Kramers–Moyal formula; Sparse identification (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:654:y:2024:i:c:s0378437124006447

DOI: 10.1016/j.physa.2024.130135

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