Gain of Entrainment in Nonlinear Cascades

[2608.15214] Gain of Entrainment in Nonlinear Cascades Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Optimization and Control arXiv:2608.15214 (math) [Submitted on 15 Aug 2026] Title: Gain of Entrainment in Nonlinear Cascades Authors: Ram Massas , Michael Margaliot View a PDF of the paper titled Gain of Entrainment in Nonlinear Cascades, by Ram Massas and Michael Margaliot View PDF HTML (experimental) Abstract: We consider the gain of entrainment (GOE)--the difference between the average steady-state output under a periodic input and the steady-state output under a constant input with the same mean--for an $n$-stage feedforward cascade of stable first-order filters interleaved with static nonlinearities. The main result is an exact decomposition of GOE as a weighted sum of local Jensen gaps, where each gap quantifies the mean shift generated by a nonlinearity, and each weight is a product of downstream incremental gains divided by linear time constants. We provide a Bregman-divergence interpretation of the decomposition, and a second-order small-amplitude of GOE separating local curvature, fluctuation energy, and differential gains. We demonstrate the theoretical results using a Michaelis-Menten cascade showing that any nonconstant periodic feeding strictly reduces the average terminal product relative to constant feeding with the same mean. Subjects: Optimization and Control (math.OC) Cite as: arXiv:2608.15214 [math.OC] (or arXiv:2608.15214v1 [math.OC] for this version) https://doi.org/10.48550/arXiv.2608.15214 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Michael Margaliot [ view email ] [v1] Sat, 15 Aug 2026 13:00:30 UTC (429 KB) Full-text links: Access Paper: View a PDF of the paper titled Gain of Entrainment in Nonlinear Cascades, by Ram Massas and Michael Margaliot View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2026-08 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Gain of Entrainment in Nonlinear Cascades#611159
• Energy Conversion and Phase Regulation in Transient States of Frequency Entrainment Described by van der Pol and Phase-Locked Loop Equations#70321
• Phase- and amplitude-dependent control of synchronization in excitatory-inhibitory networks via pulsed stimulation#612508
• Phase- and amplitude-dependent control of synchronization in excitatory-inhibitory networks via pulsed stimulation#611031
• Stochastic analysis of gradient adaptive identification of nonlinear systems with memory#630535