{"title":"与慢-快系统相比,幽灵循环在响应外部强迫时表现出更强的夹带和更丰富的动力学特征","authors":"Daniel Koch, Aneta Koseska","doi":"arxiv-2403.19624","DOIUrl":null,"url":null,"abstract":"Many natural, living and engineered systems display oscillations that are\ncharacterized by multiple timescales. Typically, such systems are described as\nslow-fast systems, where the slow dynamics result from a hyperbolic slow\nmanifold that guides the movement of the system trajectories. Recently, we have\nprovided an alternative description in which the slow dynamics result from a\nnon-hyperbolic and Lyapunov-unstable attracting sets from connected dynamical\nghosts that form a closed orbit (termed ghost cycles). Here we investigate the\nresponse properties of both type of systems to external forcing. Using the\nclassical Van-der-Pol oscillator and two modified versions of this model that\ncorrespond to a 1-ghost and a 2-ghost cycle, respectively, we find that ghost\ncycles are characterized by significant increase especially in the 1:1\nentrainment regions as demonstrated by the corresponding Arnold tongues and\nexhibit richer dynamics (bursting, chaos) in contrast to the classical\nslow-fast system. Phase plane analysis reveals that these features result from\nthe continuous remodeling of the attractor landscape of the ghost cycles models\ncharacteristic for non-autonomous systems, whereas the attractor landscape of\nthe corresponding slow-fast system remains qualitatively unaltered. We propose\nthat systems containing ghost cycles display increased flexibility and\nresponsiveness to continuous environmental changes.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"27 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Ghost cycles exhibit increased entrainment and richer dynamics in response to external forcing compared to slow-fast systems\",\"authors\":\"Daniel Koch, Aneta Koseska\",\"doi\":\"arxiv-2403.19624\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Many natural, living and engineered systems display oscillations that are\\ncharacterized by multiple timescales. Typically, such systems are described as\\nslow-fast systems, where the slow dynamics result from a hyperbolic slow\\nmanifold that guides the movement of the system trajectories. Recently, we have\\nprovided an alternative description in which the slow dynamics result from a\\nnon-hyperbolic and Lyapunov-unstable attracting sets from connected dynamical\\nghosts that form a closed orbit (termed ghost cycles). Here we investigate the\\nresponse properties of both type of systems to external forcing. Using the\\nclassical Van-der-Pol oscillator and two modified versions of this model that\\ncorrespond to a 1-ghost and a 2-ghost cycle, respectively, we find that ghost\\ncycles are characterized by significant increase especially in the 1:1\\nentrainment regions as demonstrated by the corresponding Arnold tongues and\\nexhibit richer dynamics (bursting, chaos) in contrast to the classical\\nslow-fast system. Phase plane analysis reveals that these features result from\\nthe continuous remodeling of the attractor landscape of the ghost cycles models\\ncharacteristic for non-autonomous systems, whereas the attractor landscape of\\nthe corresponding slow-fast system remains qualitatively unaltered. We propose\\nthat systems containing ghost cycles display increased flexibility and\\nresponsiveness to continuous environmental changes.\",\"PeriodicalId\":501305,\"journal\":{\"name\":\"arXiv - PHYS - Adaptation and Self-Organizing Systems\",\"volume\":\"27 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - Adaptation and Self-Organizing Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2403.19624\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Adaptation and Self-Organizing Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2403.19624","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Ghost cycles exhibit increased entrainment and richer dynamics in response to external forcing compared to slow-fast systems
Many natural, living and engineered systems display oscillations that are
characterized by multiple timescales. Typically, such systems are described as
slow-fast systems, where the slow dynamics result from a hyperbolic slow
manifold that guides the movement of the system trajectories. Recently, we have
provided an alternative description in which the slow dynamics result from a
non-hyperbolic and Lyapunov-unstable attracting sets from connected dynamical
ghosts that form a closed orbit (termed ghost cycles). Here we investigate the
response properties of both type of systems to external forcing. Using the
classical Van-der-Pol oscillator and two modified versions of this model that
correspond to a 1-ghost and a 2-ghost cycle, respectively, we find that ghost
cycles are characterized by significant increase especially in the 1:1
entrainment regions as demonstrated by the corresponding Arnold tongues and
exhibit richer dynamics (bursting, chaos) in contrast to the classical
slow-fast system. Phase plane analysis reveals that these features result from
the continuous remodeling of the attractor landscape of the ghost cycles models
characteristic for non-autonomous systems, whereas the attractor landscape of
the corresponding slow-fast system remains qualitatively unaltered. We propose
that systems containing ghost cycles display increased flexibility and
responsiveness to continuous environmental changes.