Physica D: Nonlinear Phenomena最新文献

英文中文

Topological vortex identification for two-dimensional turbulent flows in doubly periodic domains 双周期域二维湍流的拓扑涡识别

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-31 DOI: 10.1016/j.physd.2025.135099

Mitsuaki Kimura , Takeshi Matsumoto , Takashi Sakajo , Hiroshi Takeuchi , Tomoo Yokoyama

The dynamics and statistical properties of two-dimensional (2D) turbulence are often investigated through numerical simulations of incompressible, viscous fluids in doubly periodic domains. A key challenge in 2D turbulence research is accurately identifying and describing statistical properties of its coherent vortex structures within complex flow patterns. This paper addresses this challenge by providing a classification theory for the topological structure of particle orbits generated by instantaneous Hamiltonian flows on the torus

T^{2}

, which serves as a mathematical model for 2D incompressible flows. Based on this theory, we show that the global orbit structure of any Hamiltonian flow can be converted into a planar tree, named a partially Cyclically-Ordered rooted Tree (COT), and its corresponding string expression (COT representation). We apply this conversion algorithm to 2D energy and enstrophy cascade turbulence. The results show that the complex topological structure of turbulent flow patterns can be effectively represented by simple trees and sequences of letters, thereby successfully extracting coherent vortex structures and investigating their statistical properties from a topological perspective.

二维（2D）湍流的动力学和统计特性通常通过双周期域中不可压缩粘性流体的数值模拟来研究。二维湍流研究的一个关键挑战是准确识别和描述复杂流型中相干涡结构的统计特性。本文通过提供由T2环面上瞬时哈密顿流产生的粒子轨道拓扑结构的分类理论来解决这一挑战，该理论可作为二维不可压缩流的数学模型。基于这一理论，我们证明了任意哈密顿流的全局轨道结构都可以转化为平面树，称为部分循环有序根树（COT），以及相应的字符串表达式（COT表示）。我们将这种转换算法应用于二维能量和熵级联湍流。结果表明，简单的树和字母序列可以有效地表示湍流流型的复杂拓扑结构，从而成功地提取了相干涡结构，并从拓扑角度研究了它们的统计性质。

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引用次数: 0

Fundamental hydrodynamic breathers on standing waves 驻波上的基本水动力呼吸

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-30 DOI: 10.1016/j.physd.2025.135098

Yuchen He , Alexey Slunyaev , Nobuhito Mori , Ioannis Kourakis , Amin Chabchoub

Extreme wave localizations in nonlinear dispersive media, arising from modulation instability in weakly nonlinear wave interactions, can be effectively modeled by breather solutions. These breathers are exact solutions of the nonlinear Schrödinger equation and provide accurate models for understanding and controlling unidirectional rogue wave dynamics in numerical simulations or laboratory settings. A recent study by Y. He et al., Phys. Rev. Lett. 129, 144,502 (2022) offered the first proof of concept that the distinctive focusing features of Peregrine-type breathers can persist on standing water waves, consisting of two counter-propagating wave trains with identical carrier amplitudes and frequencies. In the present work, we report comprehensive experimental observations of nonlinear wave focusing dynamics on standing waves using all three fundamental breather types: the Kuznetsov-Ma, Peregrine, and Akhmediev breathers. Additionally, we extend our investigation to scenarios in which the opposing wave field has differing amplitudes or frequencies, in order to further assess the robustness of breather propagation under this particular cross-wave condition. The experimental results show good agreement with the hydrodynamic coupled nonlinear Schrödinger equation (CNLSE) for the relevant cases and confirm that both coherence and amplitude amplification of the breathers are preserved in the presence of opposing Stokes waves. These findings further support the idea that modulation instability can prevail during the interaction of distinct wave systems, even beyond the narrowband and unidirectional assumptions of the classical theory.

非线性色散介质中的极端波局域化是由弱非线性波相互作用中的调制不稳定性引起的，可以用呼吸解有效地模拟。这些呼吸器是非线性Schrödinger方程的精确解，并为在数值模拟或实验室设置中理解和控制单向流氓波动力学提供了准确的模型。Y. He等人最近的一项研究。Rev. Lett. 129,144,502（2022）提供了第一个概念证明，peregrine型呼吸器的独特聚焦特征可以在静止水波上持续存在，静止水波由两个具有相同载波振幅和频率的反向传播波列组成。在目前的工作中，我们报告了使用所有三种基本呼吸类型（库兹涅佐夫-马、佩尔格林和阿赫迈耶夫呼吸器）对驻波非线性波聚焦动力学的综合实验观察。此外，我们将研究扩展到相反波场具有不同振幅或频率的情况，以便进一步评估在这种特定的交叉波条件下呼吸传播的鲁棒性。实验结果与相关情况下的流体动力耦合非线性Schrödinger方程（CNLSE）吻合较好，并证实了在相反斯托克斯波存在下，呼吸波的相干性和振幅放大都保持不变。这些发现进一步支持了这样一种观点，即调制不稳定性可以在不同波系统的相互作用中盛行，甚至超出了经典理论的窄带和单向假设。

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引用次数: 0

Nonlinear dynamics of periodic Lugiato-Lefever waves against sums of co-periodic and localized perturbations 周期Lugiato-Lefever波对共周期和局域扰动和的非线性动力学

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-23 DOI: 10.1016/j.physd.2025.135079

Joannis Alexopoulos

In recent years, essential progress has been made in the nonlinear stability analysis of periodic Lugiato-Lefever waves against co-periodic and localized perturbations. Inspired by considerations from fiber optics, we introduce a novel iteration scheme which allows to perturb against sums of co-periodic and localized functions. This unifies previous stability theories in a natural manner.

近年来，周期Lugiato-Lefever波对共周期和局域扰动的非线性稳定性分析取得了重要进展。受光纤的启发，我们引入了一种新的迭代方案，它允许对共周期函数和局域函数的和进行摄动。这自然地统一了以前的稳定性理论。

引用次数: 0

A Hamiltonian approach for point vortices on non-orientable surfaces 非定向曲面上点涡的哈密顿方法

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-20 DOI: 10.1016/j.physd.2025.135084

N. Balabanova , J.A. Montaldi

We investigate the motion of point vortices on the Möbius band and Klein bottle. Since these are non-orientable surfaces, the standard Hamiltonian approach does not apply. We therefore begin by establishing a modified Hamiltonian approach which works for arbitrary non-orientable surfaces, through describing the phase space, the Hamiltonian and the local equations of motion. We use a combination of twisted functions and oriented double covers to adapt some of the known notions of vortex dynamics to non-orientable surfaces. For both of the surfaces of interest, we write Hamiltonian-type equations of vortex motion explicitly and follow that by the description of relative equilibria and an investigation of the motion of one and two vortices.

我们研究了点涡在Möbius带和克莱因瓶上的运动。因为这些是不可定向的表面，所以标准哈密顿方法不适用。因此，我们首先通过描述相空间、哈密顿量和局部运动方程，建立一种适用于任意非定向曲面的修正哈密顿方法。我们使用扭曲函数和定向双盖的组合来适应一些已知的涡旋动力学的概念，以适应不可定向的表面。对于这两个感兴趣的曲面，我们明确地写出了涡旋运动的哈密顿方程，并通过描述相对平衡和研究一个和两个涡旋的运动来遵循它。

引用次数: 0

Late-time growth of an inhomogeneous, turbulent mixing layer subjected to transient compression 受瞬态压缩的非均匀湍流混合层的后期增长

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-20 DOI: 10.1016/j.physd.2025.135056

Bradley Pascoe , Michael Groom , Ben Thornber

Recent engineering models of turbulent mixing layers under strain imply that there may be a permanent modification of important mixing layer physics following a temporary application of strain. This paper presents a set of Implicit Large-Eddy Simulations of a canonical Richtmyer-Meshkov instability to explore the validity of this model result. The well-characterised θ-group quarter scale case is modified to include a strain rate which halves domain widths in approximately five eddy turnover times. Following the removal of strain, the observed value of the growth rate exponent

θ = 0.112

which is a 2.5 times reduction compared with the unstrained case. Whilst θ is slowly rising at late time, the actual change in θ is qualitatively in good agreement with the engineering model but is quantitatively a much greater change than expected. Mixedness also increases significantly, from

Θ = 0.8

for the unstrained to

Θ = 0.9

following the application of strain. Turbulent kinetic energy substantially rises during strain, but then dissipates more rapidly following the removal of strain due to the decreased turbulent length-scales. Overall these results demonstrate that modifications to engineering models, such as those proposed by Pascoe et al. (Phys. Rev. Fluids 10 (6), 064609, 2025) are needed to capture these significant variations in flow physics which persist even following the removal of strain. The engineering model further predicts more substantial impacts at high overall compression or expansion as expected in typical applications in inertial confinement fusion, supernovae or explosions.

应变作用下湍流混合层的最新工程模型表明，在临时施加应变后，重要的混合层物理可能会发生永久性的改变。本文给出了典型richhtmyer - meshkov不稳定性的一组隐式大涡模拟，以探讨该模型结果的有效性。特征良好的θ-群四分之一尺度情况被修改为包括在大约五个涡流周转时间内将域宽度减半的应变率。去除应变后，生长速率指数θ的观测值为0.112，与未应变情况相比降低了2.5倍。当θ在后期缓慢上升时，θ的实际变化在质量上与工程模型很好地一致，但在数量上比预期的变化要大得多。混合度也显著增加，从未应变的Θ=0.8到施加应变后的Θ=0.9。在应变过程中，湍流动能大幅上升，但在去除应变后，由于湍流长度尺度的减小，湍流动能消散得更快。总的来说，这些结果表明对工程模型的修改，如Pascoe等人提出的那些。Rev. fluid 10(6), 064609, 2025)需要捕捉这些流动物理的显著变化，即使在去除应变后仍然存在。工程模型进一步预测了在高总体压缩或膨胀时的更大影响，正如在惯性约束聚变、超新星或爆炸的典型应用中所期望的那样。

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引用次数: 0

Machine learning techniques to identify synchronization patterns in multiple timescale dynamical systems networks 识别多时间尺度动态系统网络同步模式的机器学习技术

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-17 DOI: 10.1016/j.physd.2025.135082

A. Bandera , S. Fernández-García , M. Gómez-Mármol , A. Vidal

We present a novel methodology that combines machine learning techniques with dynamical analysis to classify and interpret the behavior distribution of network models of coupled dynamical systems. Our methodology determines the optimal number of distinct behaviors and classifies them based on time-series features, allowing for an interpretable and automated partition of the parameter space. Applying this approach to a homogeneous two-clusters model of intracellular calcium concentration dynamics, we identify nine different long-term behaviors, including complex and chaotic regimes, mapping experimental data available in the literature. The results highlight the complementarity between data-driven classification and classical dynamical analysis in capturing rich synchronization patterns and detecting subtle transitions in multiple timescale biological systems.

我们提出了一种新的方法，将机器学习技术与动态分析相结合，对耦合动力系统网络模型的行为分布进行分类和解释。我们的方法确定了不同行为的最佳数量，并根据时间序列特征对它们进行分类，从而允许对参数空间进行可解释和自动划分。将这种方法应用于细胞内钙浓度动力学的同质双簇模型，我们确定了九种不同的长期行为，包括复杂和混沌制度，并绘制了文献中可用的实验数据。结果强调了数据驱动分类与经典动态分析在捕获丰富的同步模式和检测多时间尺度生物系统的微妙转变方面的互补性。

引用次数: 0

JostONet: A neural operator architecture for solving the Jost solution and scattering coefficients of the Schrödinger spectral problem JostONet：用于求解Schrödinger光谱问题的Jost解和散射系数的神经算子架构

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-16 DOI: 10.1016/j.physd.2025.135073

Zhengwu Miao , Yong Chen

The Schrödinger spectral problem is a central topic in mathematical physics. In numerical inverse scattering transform (NIST), the reflection coefficient R(k) contained in the scattering data

S

must be repeatedly computed by solving the spectral problem at discrete wave number k. We propose a novel neural operator framework, the Jost operator network (JostONet), for fast inference of the Jost solution and its associated R(k), offering a promising alternative for computing R(k) in the NIST. JostONet is composed of three specialized modules: (i) High-energy region

R_{h}

: inspired by the asymptotic behavior of the Jost solution, a novel amplitude decomposition is derived, based on which a variable amplitude operator network is constructed. Normalization conditions and conservation property are embedded in the loss function, and hard boundary constraints are imposed. (ii) Intermediate-energy region

R_{m}

: The wave number k is treated as a degenerate functional variable, and a wave function operator network is constructed based on the multi-input operator network. (iii) Low-energy region

R_{l}

: a perturbation-wave function operator network is introduced, which exploits the perturbation expansion of the Jost solution with respect to k and is composed of a sequence of Deep Operator Networks. During training, a novel function space

{\tilde{H}}^{κ, η} (R)

is constructed based on Hermite polynomials to generate potential functions with Gaussian decay, which serve as inputs to the neural operators. JostONet achieves satisfactory predictive accuracy across all energy regions, with an inference speed at least an order of magnitude faster than traditional methods, and it is capable of generalizing to higher-order potentials in the space

{\tilde{H}}^{κ, η} (R)

. In addition, we provide theoretical support and extensive numerical validation for the partitioning of k, along with detailed numerical analysis of each module.

Schrödinger光谱问题是数学物理中的一个中心问题。在数值逆散射变换（NIST）中，散射数据S中包含的反射系数R(k)必须通过求解离散波数k处的光谱问题来重复计算。我们提出了一种新的神经算子框架——Jost算子网络（JostONet），用于快速推断Jost解及其相关的R(k)，为NIST中R(k)的计算提供了一种有希望的替代方案。JostONet由三个专用模块组成：(1)高能区域Rh：根据Jost解的渐近特性，推导出一种新的振幅分解，并在此基础上构造变振幅算子网络。在损失函数中嵌入归一化条件和守恒性质，并施加硬边界约束。（ii）中能量区域Rm：将波数k作为退化泛函变量，在多输入算子网络的基础上构建波函数算子网络。（iii）低能区域Rl：引入了一个微扰波函数算子网络，它利用Jost解对k的微扰展开，由一系列深度算子网络组成。在训练过程中，基于Hermite多项式构造一个新的函数空间H ~ κ，η(R)，生成具有高斯衰减的势函数，作为神经算子的输入。JostONet在所有能量区域都达到了令人满意的预测精度，其推理速度至少比传统方法快一个数量级，并且能够推广到空间H ~ κ，η(R)中的高阶电位。此外，我们为k的划分提供了理论支持和广泛的数值验证，并对每个模块进行了详细的数值分析。

{"title":"JostONet: A neural operator architecture for solving the Jost solution and scattering coefficients of the Schrödinger spectral problem","authors":"Zhengwu Miao , Yong Chen","doi":"10.1016/j.physd.2025.135073","DOIUrl":"10.1016/j.physd.2025.135073","url":null,"abstract":"<div><div>The Schrödinger spectral problem is a central topic in mathematical physics. In numerical inverse scattering transform (NIST), the reflection coefficient <em>R</em>(<em>k</em>) contained in the scattering data <span><math><mi>S</mi></math></span> must be repeatedly computed by solving the spectral problem at discrete wave number <em>k</em>. We propose a novel neural operator framework, the Jost operator network (JostONet), for fast inference of the Jost solution and its associated <em>R</em>(<em>k</em>), offering a promising alternative for computing <em>R</em>(<em>k</em>) in the NIST. JostONet is composed of three specialized modules: (i) High-energy region <span><math><msub><mi>R</mi><mi>h</mi></msub></math></span>: inspired by the asymptotic behavior of the Jost solution, a novel amplitude decomposition is derived, based on which a variable amplitude operator network is constructed. Normalization conditions and conservation property are embedded in the loss function, and hard boundary constraints are imposed. (ii) Intermediate-energy region <span><math><msub><mi>R</mi><mi>m</mi></msub></math></span>: The wave number <em>k</em> is treated as a degenerate functional variable, and a wave function operator network is constructed based on the multi-input operator network. (iii) Low-energy region <span><math><msub><mi>R</mi><mi>l</mi></msub></math></span>: a perturbation-wave function operator network is introduced, which exploits the perturbation expansion of the Jost solution with respect to <em>k</em> and is composed of a sequence of Deep Operator Networks. During training, a novel function space <span><math><mrow><msup><mover><mrow><mi>H</mi></mrow><mo>˜</mo></mover><mrow><mi>κ</mi><mo>,</mo><mi>η</mi></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> is constructed based on Hermite polynomials to generate potential functions with Gaussian decay, which serve as inputs to the neural operators. JostONet achieves satisfactory predictive accuracy across all energy regions, with an inference speed at least an order of magnitude faster than traditional methods, and it is capable of generalizing to higher-order potentials in the space <span><math><mrow><msup><mover><mrow><mi>H</mi></mrow><mo>˜</mo></mover><mrow><mi>κ</mi><mo>,</mo><mi>η</mi></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span>. In addition, we provide theoretical support and extensive numerical validation for the partitioning of <em>k</em>, along with detailed numerical analysis of each module.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"486 ","pages":"Article 135073"},"PeriodicalIF":2.9,"publicationDate":"2025-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145840767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Chaos and order in drift double layers: Nonlinear dynamics in epi plasmas with adiabatic trapping 漂移双层中的混沌与有序：具有绝热俘获的外等离子体的非线性动力学

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-14 DOI: 10.1016/j.physd.2025.135083

M.A. Rehman , M.J. Iqbal , Zeeshan Iqbal , H.A. Shah

The effect of adiabatic trapping in electron-positron-ion (epi) plasmas plays a crucial role in the formation and evolution of drift double-layer (DL) structures, with significant implications for both space and laboratory plasmas. In this study, we investigate the influence of adiabatic trapping, a microscopic phenomenon, on the evolution of drift DLs in epi plasma. Using the Sagdeev potential method, we investigate the conditions necessary to form electrostatic drift DL solutions in epitaxial plasma. Our analysis reveals that key parameters, such as positron concentration, ion drift speed, and the electron-to-positron temperature ratio, significantly influence the formation of drift DLs and their nonlinear characteristics. Notably, only compressive drift DLs are observed, with their amplitude varying based on changes in plasma parameters. Furthermore, the nonlinear dynamical response of the system to external periodic forcing exhibits a rich spectrum of behaviors, including periodic (e.g., period-2 and period-3), quasiperiodic, and chaotic regimes. To the best of our knowledge, this is the first study to conduct a nonlinear dynamical analysis of drift double layers in epi plasmas under external periodic forcing while incorporating adiabatic trapping effects. This work provides new insights into the interplay of microphysical trapping and external drivers in shaping nonlinear plasma structures, thereby advancing the understanding of DL dynamics in space, astrophysical, and laboratory environments.

电子-正电子-离子（epi）等离子体中的绝热俘获效应在漂移双层（DL）结构的形成和演化中起着至关重要的作用，对空间和实验室等离子体都具有重要意义。在本研究中，我们研究了绝热阱这一微观现象对外皮等离子体中漂移DLs演化的影响。利用Sagdeev电位方法，研究了外延等离子体中形成静电漂移DL溶液的必要条件。分析表明，正电子浓度、离子漂移速度、电子与正电子温度比等关键参数对漂移dl的形成及其非线性特性有显著影响。值得注意的是，仅观察到压缩漂移dl，其振幅随等离子体参数的变化而变化。此外，系统对外部周期强迫的非线性动力学响应表现出丰富的行为谱，包括周期（例如，周期2和周期3）、准周期和混沌状态。据我们所知，这是第一个在考虑绝热俘获效应的情况下，对外周期强迫下外等离子体中漂移双层进行非线性动力学分析的研究。这项工作为形成非线性等离子体结构的微物理捕获和外部驱动因素的相互作用提供了新的见解，从而促进了对空间、天体物理和实验室环境中DL动力学的理解。

{"title":"Chaos and order in drift double layers: Nonlinear dynamics in epi plasmas with adiabatic trapping","authors":"M.A. Rehman , M.J. Iqbal , Zeeshan Iqbal , H.A. Shah","doi":"10.1016/j.physd.2025.135083","DOIUrl":"10.1016/j.physd.2025.135083","url":null,"abstract":"<div><div>The effect of adiabatic trapping in electron-positron-ion (<em>epi</em>) plasmas plays a crucial role in the formation and evolution of drift double-layer (<em>DL</em>) structures, with significant implications for both space and laboratory plasmas. In this study, we investigate the influence of adiabatic trapping, a microscopic phenomenon, on the evolution of drift <em>DLs</em> in <em>epi</em> plasma. Using the Sagdeev potential method, we investigate the conditions necessary to form electrostatic drift DL solutions in epitaxial plasma. Our analysis reveals that key parameters, such as positron concentration, ion drift speed, and the electron-to-positron temperature ratio, significantly influence the formation of drift <em>DLs</em> and their nonlinear characteristics. Notably, only compressive drift <em>DLs</em> are observed, with their amplitude varying based on changes in plasma parameters. Furthermore, the nonlinear dynamical response of the system to external periodic forcing exhibits a rich spectrum of behaviors, including periodic (e.g., period-2 and period-3), quasiperiodic, and chaotic regimes. To the best of our knowledge, this is the first study to conduct a nonlinear dynamical analysis of drift double layers in <em>epi</em> plasmas under external periodic forcing while incorporating adiabatic trapping effects. This work provides new insights into the interplay of microphysical trapping and external drivers in shaping nonlinear plasma structures, thereby advancing the understanding of <em>DL</em> dynamics in space, astrophysical, and laboratory environments.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"487 ","pages":"Article 135083"},"PeriodicalIF":2.9,"publicationDate":"2025-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145766054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Critical noise for advanced dynamic B-tipping in nearly non-smooth Stommel-type models 近非光滑stommel型模型先进动态b倾转的临界噪声

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-13 DOI: 10.1016/j.physd.2025.135055

Chris Budd , Rachel Kuske

We study critical relationships between the smoothness parameter for the underlying fold bifurcation and the noise level in the context of B-tipping near smooth and non-smooth dynamic fold bifurcations. The motivation is the Stommel 2-box model, a piecewise-smooth continuous dynamical system modeling thermohaline circulation in the North Atlantic, and related climate models. These contain non-smooth fold bifurcations which arise when a saddle-point and a stable focus meet at a border collision bifurcation. An asymptotic analysis of the corresponding Fokker-Planck Equation (FPE) for the stochastic system provides insight into critical noise levels, depending on the relative rate of parameter variation and a measure of smoothness of the underlying bifurcation. Critical scales are obtained from different reductions of the FPE, identifying cases where noise may advance tipping relative to deterministic behavior. Applying this approach for B-tipping near both smooth and non-smooth folds shows that the non-smooth case has greater sensitivity to smaller noise levels, with a smaller critical scale for noise-advanced tipping in the non-smooth case. Since these results do not depend on obtaining a solution of the FPE, the approach can be adapted to multi-degree-of-freedom models and in other applications.

研究了在光滑和非光滑动态褶皱分岔附近的B-tipping情况下，底层褶皱分岔的平滑参数与噪声级之间的临界关系。其动机是Stommel 2-box模式（一个模拟北大西洋热盐环流的逐段平滑连续动力系统）和相关气候模式。这些包括非光滑褶皱分岔，当鞍点和稳定焦点在边界碰撞分岔处相遇时产生。对随机系统相应的福克-普朗克方程（FPE）的渐近分析提供了对临界噪声水平的洞察，这取决于参数变化的相对速率和潜在分岔的平滑度。从FPE的不同减少中获得临界尺度，确定噪声可能相对于确定性行为提前引爆的情况。将该方法应用于光滑和非光滑折叠附近的b -倾爆表明，非光滑情况对较小的噪声水平具有更高的灵敏度，非光滑情况下噪声超前倾爆的临界尺度较小。由于这些结果不依赖于获得FPE的解，因此该方法可以适用于多自由度模型和其他应用。

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引用次数: 0

Sequential clearing dynamics and systemic risk control for multilayer financial system 多层次金融系统的顺序清算动态与系统性风险控制

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-13 DOI: 10.1016/j.physd.2025.135081

Yi Ding , Chun Yan , Wei Liu , Jiahui Liu

Risk contagion in financial systems presents spatially hierarchical patterns and temporally nonlinear accumulation. To explore this dynamic contagion process, this paper constructs a multilayer dynamic financial network incorporating three types of interbank interactions: interbank lending, cross-holding, and overlapping investment portfolios. We extend the classical Eisenberg-NOE clearing model to a multiplex and sequential dynamic setting, characterizing the propagation of risk through nonlinear clearing dynamics. Bank defaults are classified into illiquidity and insolvency, with temporal evolution achieved through deferred debt. Next, we model the government control as a Markov decision process and introduce fairness constraints to balance systemic stability and equity. Finally, we use Monte Carlo simulations to analyze the numerical results obtained with different control strategies and provide robustness tests.

金融体系的风险传染表现出空间分层模式和时间非线性累积。为了探讨这一动态传染过程，本文构建了一个包含三种类型银行间相互作用的多层动态金融网络：银行间借贷、交叉持有和重叠投资组合。我们将经典的Eisenberg-NOE清算模型推广到多路序列动态环境中，通过非线性清算动力学表征风险的传播。银行违约分为流动性不足和资不抵债，通过递延债务实现时间演化。其次，我们将政府控制建模为马尔可夫决策过程，并引入公平约束来平衡系统稳定性和公平性。最后，利用蒙特卡罗仿真对不同控制策略下的数值结果进行了分析，并进行了鲁棒性测试。

引用次数: 0

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