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We hence focus on the discrete host\u2013parasitoid Beddington\u2013Free\u2013Lawton model and show that a more comprehensive mathematical study of the dynamics behind the onset of on\u2013off intermittency in host\u2013parasitoid systems may be achieved by considering a deterministic, chaotic system that represents the dynamics of the environment. To this aim, some of the key model parameters are allowed to vary in time according to an evolution law that can exhibit chaotic behavior. Fixed points and stability properties of the resulting 3D nonlinear discrete dynamical system are investigated and on\u2013off intermittency is found to emerge strictly above the blowout bifurcation threshold. We show, however, that, in some cases, this phenomenon can also emerge in the sub-threshold. We hence introduce the novel concept of long-term reactivity and show that it can be considered as a necessary condition for the onset of on\u2013off intermittency. Investigations in the time-dependent regimes and kurtosis maps are provided to support the above results. Our study also suggests how important it is to carefully monitor environmental variability caused by random fluctuations in natural factors or by anthropogenic disturbances in order to minimize its effects on throphic interactions and protect the potential function of parasitoids as biological control agents. <\/jats:p>","DOI":"10.1142\/s021812742450041x","type":"journal-article","created":{"date-parts":[[2024,3,13]],"date-time":"2024-03-13T23:55:05Z","timestamp":1710374105000},"source":"Crossref","is-referenced-by-count":3,"title":["On\u2013Off Intermittency and Long-Term Reactivity in a Host\u2013Parasitoid Model with a Deterministic Driver"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4846-2795","authenticated-orcid":false,"given":"Fasma","family":"Diele","sequence":"first","affiliation":[{"name":"Istituto per le Applicazioni del Calcolo \u2018M.Picone\u2019, Consiglio Nazionale delle Ricerche, via G. 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