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In this paper, a strongly nonlinear energy harvesting system with time delay is taken as the research object. To address the above difficulties, an extended stochastic averaging method is proposed to investigate the time delay induced stochastic dynamics of the system. The energy-dependent frequency is first constructed according to the operating mechanism of the multi-well potential function. Then, the stochastic averaging method of energy envelope is extended to derive analytical expressions for the stationary probability density and the mean output power. Finally, the effects of time delay parameters on the stationary response and the mean output power are analyzed in detail. Results show that even small time delays cannot be ignored in practical applications, as both the time-delayed feedback gain and the time delay have significant influences on the dynamic characteristics of systems. Moreover, adopting appropriate time-delayed feedback control can markedly enhance system performance. The effectiveness of the extended stochastic averaging method is verified through Monte Carlo numerical simulations.<\/jats:p>","DOI":"10.1063\/5.0335813","type":"journal-article","created":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T12:58:13Z","timestamp":1777985893000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Time delay induced stochastic dynamics in a strongly nonlinear energy harvesting system"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4925-9905","authenticated-orcid":false,"given":"Yanxia","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Sciences, Xi'an University of Science and Technology 1 , Xi'an 710054, Shaanxi,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-6999-1408","authenticated-orcid":false,"given":"Shaoyi","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Sciences, Xi'an University of Science and Technology 1 , Xi'an 710054, Shaanxi,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5537-5684","authenticated-orcid":false,"given":"Yanfei","family":"Jin","sequence":"additional","affiliation":[{"name":"Department of Mechanics, Beijing Institute of Technology 2 , Beijing 100081,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2026,5,5]]},"reference":[{"key":"2026050508580684000_c1","doi-asserted-by":"publisher","first-page":"118158","DOI":"10.1016\/j.chaos.2026.118158","article-title":"The influence of delay time on the generation of chaotic oscillations in a two-dimensional resonant system","volume":"208","year":"2026","journal-title":"Chaos, Solitons Fractals"},{"issue":"12","key":"2026050508580684000_c2","doi-asserted-by":"publisher","first-page":"121104","DOI":"10.1063\/5.0305531","article-title":"A systematic delayed feedback control approach for unstable periodic orbits in chaotic systems with unknown parameters","volume":"35","year":"2025","journal-title":"Chaos"},{"key":"2026050508580684000_c3","doi-asserted-by":"publisher","first-page":"129150","DOI":"10.1016\/j.amc.2024.129150","article-title":"Improving disturbance rejection and tracking performance of interval type-2T-S fuzzy systems with time-varying delay","volume":"489","year":"2025","journal-title":"Appl. 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