An Idealized Delay-Differential Model of Scuba Diver Porpoising and Runaway Ascent

[2608.14978] An Idealized Delay-Differential Model of Scuba Diver Porpoising and Runaway Ascent Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Nonlinear Sciences > Chaotic Dynamics arXiv:2608.14978 (nlin) [Submitted on 15 Aug 2026] Title: An Idealized Delay-Differential Model of Scuba Diver Porpoising and Runaway Ascent Authors: Sandy Hardian Susanto Herho , Faizal Ade Rahmahuddin Abdullah , Iwan Pramesti Anwar , Faruq Khadami , Alfita Puspa Handayani , Karina Aprilia Sujatmiko , Rusmawan Suwarman , Dasapta Erwin Irawan View a PDF of the paper titled An Idealized Delay-Differential Model of Scuba Diver Porpoising and Runaway Ascent, by Sandy Hardian Susanto Herho and Faizal Ade Rahmahuddin Abdullah and Iwan Pramesti Anwar and Faruq Khadami and Alfita Puspa Handayani and Karina Aprilia Sujatmiko and Rusmawan Suwarman and Dasapta Erwin Irawan View PDF HTML (experimental) Abstract: A scuba diver holding constant depth balances on an unstable equilibrium: the gas carried in the suit and buoyancy compensator compresses with depth, so the buoyant force falls as the diver sinks and rises as the diver ascends. We represent the diver as a proportional-derivative controller that regulates this compressible-buoyancy saddle after a finite reaction delay, and we derive the governing delay differential equation from the vertical force balance and the isothermal gas law, reducing it to a damping ratio, two control gains, and a dimensionless delay. The characteristic spectrum, obtained by pseudospectral collocation of the semigroup generator and checked against a direct Newton solution of the characteristic equation, locates the Hopf boundary that separates stable hovering from sustained porpoising; for the baseline diver the critical reaction delay is 3.36 s and the onset period is 28.8 s. The bifurcation is supercritical, and because the saturating force is the quadratic hydrodynamic drag, the limit-cycle amplitude grows in proportion to the delay excess rather than as its square root. The safe-operating envelope shows that runaway ascent is triggered by saturation of the compensator, not by loss of linear stability, so a stable and an unstable diver can share the same escape threshold. As onset is approached, the lag-one autocorrelation and variance rise while the fitted recovery rate falls and matches the spectral abscissa, giving an eigenvalue-exact early warning of the transition. Comments: 19 pages, 10 figures Subjects: Chaotic Dynamics (nlin.CD) ; Systems and Control (eess.SY); Dynamical Systems (math.DS); Biological Physics (physics.bio-ph) MSC classes: 34K18, 34K20, 34K13, 34K28, 93D15, 94A17 Cite as: arXiv:2608.14978 [nlin.CD] (or arXiv:2608.14978v1 [nlin.CD] for this version) https://doi.org/10.48550/arXiv.2608.14978 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Sandy Herho [ view email ] [v1] Sat, 15 Aug 2026 02:17:13 UTC (226 KB) Full-text links: Access Paper: View a PDF of the paper titled An Idealized Delay-Differential Model of Scuba Diver Porpoising and Runaway Ascent, by Sandy Hardian Susanto Herho and Faizal Ade Rahmahuddin Abdullah and Iwan Pramesti Anwar and Faruq Khadami and Alfita Puspa Handayani and Karina Aprilia Sujatmiko and Rusmawan Suwarman and Dasapta Erwin Irawan View PDF HTML (experimental) TeX Source view license Current browse context: nlin.CD < prev | next > new | recent | 2026-08 Change to browse by: cs cs.SY eess eess.SY math math.DS nlin physics physics.bio-ph References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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