{"title":"Higher order mass aggregation terms in a nonlinear predator–prey model maintain limit cycle stability in Saturn’s F ring","authors":"","doi":"10.1016/j.physd.2024.134311","DOIUrl":null,"url":null,"abstract":"<div><p>We consider a generic higher order mass aggregation term for interactions between particles exhibiting oscillatory clumping and disaggregation behavior in the F ring of Saturn, using a novel predator–prey model that relates the mean mass aggregate (prey) and the square of the relative dispersion velocity (predator) of the interacting particles. The resulting cyclic dynamic behavior is demonstrated through time series plots, phase portraits and their stroboscopic phase maps.</p><p>Employing an eigenvalue stability analysis of the Jacobian of the system, we find out that there are two distinct regimes depending on the exponent and the amplitude of the higher order interactions of the nonlinear mass term. In particular, the system exhibits a limit cycle oscillatory stable behavior for a range of values of these parameters and a non-cyclic behavior for another range, separated by a curve across which phase transitions would occur between the two regimes. This shows that the observed clumping dynamics in Saturn’s F ring, corresponding to a limit cycle stability regime, can be systematically maintained in presence of physical higher order mass aggregation terms in the introduced model.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7000,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167278924002628/pdfft?md5=c64de23a9fa9a2db870b09586c802e39&pid=1-s2.0-S0167278924002628-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica D: Nonlinear Phenomena","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167278924002628","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We consider a generic higher order mass aggregation term for interactions between particles exhibiting oscillatory clumping and disaggregation behavior in the F ring of Saturn, using a novel predator–prey model that relates the mean mass aggregate (prey) and the square of the relative dispersion velocity (predator) of the interacting particles. The resulting cyclic dynamic behavior is demonstrated through time series plots, phase portraits and their stroboscopic phase maps.
Employing an eigenvalue stability analysis of the Jacobian of the system, we find out that there are two distinct regimes depending on the exponent and the amplitude of the higher order interactions of the nonlinear mass term. In particular, the system exhibits a limit cycle oscillatory stable behavior for a range of values of these parameters and a non-cyclic behavior for another range, separated by a curve across which phase transitions would occur between the two regimes. This shows that the observed clumping dynamics in Saturn’s F ring, corresponding to a limit cycle stability regime, can be systematically maintained in presence of physical higher order mass aggregation terms in the introduced model.
期刊介绍:
Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.