Unraveling multiple 1:1 entrainment regions in the Arnold onion diagram: A study of the circadian Novak–Tyson model

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2025-09-24 DOI:10.1016/j.physd.2025.134949

Emel Khan , Lawan Wijayasooriya , Pejman Sanaei

{"title":"Unraveling multiple 1:1 entrainment regions in the Arnold onion diagram: A study of the circadian Novak–Tyson model","authors":"Emel Khan , Lawan Wijayasooriya , Pejman Sanaei","doi":"10.1016/j.physd.2025.134949","DOIUrl":null,"url":null,"abstract":"<div><div>The entrainment of biological oscillators is a fundamental problem in studying dynamical systems and synchronization. The Arnold onion diagram is a key tool for visualizing entrainment patterns in a two-dimensional parameter space, defined by period (<span><math><mi>T</mi></math></span>) and photoperiod (<span><math><mi>χ</mi></math></span>). This paper investigates the entrainment behavior of various oscillatory regimes in the Novak–Tyson (NT) model. While previous studies have documented the presence of Arnold onions featuring a single 1:1 entrainment region, our work introduces the novel emergence of multiple disconnected 1:1 entrainment regions within these diagrams. Through the analysis of dynamical systems, we show that multiple Arnold onions emerge for an unforced system near the Hopf bifurcation, which behaves as a damped oscillator. These findings offer new insights into the complex mechanisms underlying circadian seasonality and its dependence on intrinsic oscillator dynamics.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"483 ","pages":"Article 134949"},"PeriodicalIF":2.9000,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica D: Nonlinear Phenomena","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167278925004269","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

The entrainment of biological oscillators is a fundamental problem in studying dynamical systems and synchronization. The Arnold onion diagram is a key tool for visualizing entrainment patterns in a two-dimensional parameter space, defined by period (

T

) and photoperiod (

χ

). This paper investigates the entrainment behavior of various oscillatory regimes in the Novak–Tyson (NT) model. While previous studies have documented the presence of Arnold onions featuring a single 1:1 entrainment region, our work introduces the novel emergence of multiple disconnected 1:1 entrainment regions within these diagrams. Through the analysis of dynamical systems, we show that multiple Arnold onions emerge for an unforced system near the Hopf bifurcation, which behaves as a damped oscillator. These findings offer new insights into the complex mechanisms underlying circadian seasonality and its dependence on intrinsic oscillator dynamics.

查看原文本刊更多论文

在阿诺德洋葱图中解开多个1:1的携带区域：昼夜节律诺瓦克-泰森模型的研究

生物振子的夹带是研究动力系统和同步的一个基本问题。阿诺德洋葱图是在二维参数空间中可视化夹带模式的关键工具，由周期(T)和光周期（χ）定义。本文研究了Novak-Tyson （NT）模型中不同振荡状态的夹带行为。虽然以前的研究已经记录了阿诺德洋葱具有单个1:1夹带区域的存在，但我们的工作在这些图中引入了多个不连接的1:1夹带区域的新出现。通过对动力系统的分析，我们证明了在Hopf分岔附近的非强制系统存在多个Arnold onion，其表现为阻尼振荡器。这些发现为昼夜节律季节性的复杂机制及其对内在振荡器动力学的依赖提供了新的见解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

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.