SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS (SIADS) 发表关于动力系统的数学分析和建模及其在物理、工程、生命和社会科学中的应用的研究文章。 SIADS 仅以电子格式发布。

The SIAM Journal on Applied Dynamical Systems (SIADS) publishes research articles on the mathematical analysis and modeling of dynamical systems and their applications in physics, engineering, life sciences, and social sciences. SIADS is published exclusively in electronic format.

SIAM Journal on Applied Dynamical Systems (SIADS) 发表关于动力系统的数学分析、建模及其在物理、工程、生命科学和社会科学中的应用研究文章。SIADS 仅以电子格式发布。

SIAM Journal on Applied Dynamical Systems

West Nile virus (WNv) is a mosquito-borne disease caused by Flavivirus. To investigate the combined effects of vertical transmission, temperature-dependent incubation periods and seasonality on the transmission of WNv, we develop a delay differential system with stage-structure and time-varying delays. We then derive the mosquito reproduction number $\mathcal{R}_0^V$ and basic reproduction number $\mathcal{R}_0$ and show that these two numbers serve as threshold parameters that determine whether WNv will spread. As an application, we conduct a case study for WNv transmission in Los Angeles County, California. We also carry out numerical simulations to identify the situations that require time-periodic delays. Moreover, we find that rising temperatures may potentially increase the risk of disease outbreaks.

Feng-Bin Wang

Ruiwen Wu

Xiao-Qiang Zhao

A West Nile Virus Transmission Model with Periodic Incubation Periods

When a vector field in $\mathbb{R}^3$ is discontinuous on a smooth codimension one surface, it may be simultaneously tangent to both sides of the surface at generic isolated points (singularities). For a piecewise-smooth dynamical system governed by the vector field, we show that the local dynamics depends on a single quantity—the jump in direction of the vector field through the singularity. This quantity controls a bifurcation, in which the initially repelling singularity becomes the apex of a pair of parabolic invariant surfaces. The surfaces are smooth except where they intersect the discontinuity surface, and they divide local space into regions of attraction to, and repulsion from, the singularity.

Mike R. Jeffrey

Alessandro Colombo

The Two-Fold Singularity of Discontinuous Vector Fields

不连续向量场的二重奇异性

At a two-fold singularity, the velocity vector of a flow switches discontinuously across a codimension one switching manifold, between two directions that both lie tangent to the manifold. Particularly intricate dynamics arises when the local flow curves toward the switching manifold from both sides, a case referred to as the Teixeira singularity. The flow locally performs two different actions: it winds around the singularity by crossing repeatedly through, and passes through the singularity by sliding along, the switching manifold. The case when the number of rotations around the singularity is infinite has been analyzed in detail. Here we study the case when the flow makes a finite, but previously unknown, number of rotations around the singularity between incidents of sliding. We show that the solution is remarkably simple: the maximum and minimum numbers of rotations made anywhere in the flow differ only by one and increase incrementally with a single parameter---the angular jump in the flow direction across the switching manifold at the singularity.

S. Fernández-García

D. Angulo García

G. Olivar Tost

M. di Bernardo

M. R. Jeffrey

Structural Stability of the Two-Fold Singularity

两重奇异点的结构稳定性

A vector field is piecewise smooth if its value jumps across a hypersurface, and a two-fold singularity is a point where the flow is tangent to the hypersurface from both sides. Two-folds are generic in piecewise smooth systems of three or more dimensions. We derive the local dynamics of all possible two-folds in three dimensions, including nonlinear effects around certain bifurcations, finding that they admit a flow exhibiting chaotic but nondeterministic dynamics. In cases where the flow passes through the two-fold, upon reaching the singularity it is unique in neither forward nor backward time, meaning the causal link between inward and outward dynamics is severed. In one scenario this occurs recurrently. The resulting flow makes repeated, but nonperiodic, excursions from the singularity, whose path and amplitude is not determined by previous excursions. We show that this behavior is robust and has many of the properties associated with chaos. Local geometry reveals that the chaotic behavior can be eliminated by varying a single parameter: the angular jump of the vector field across the two-fold.

Nondeterministic Chaos, and the Two-fold Singularity in Piecewise Smooth Flows

非确定性混沌与分段光滑流中的双重奇异性

A major challenge in the study of dynamical systems is that of model discovery: turning data into models that are not just predictive, but provide insight into the nature of the underlying dynamical system that generated the data. This problem is made more difficult by the fact that many systems of interest exhibit diverse behaviors across multiple time scales. We introduce a number of data-driven strategies for discovering nonlinear multiscale dynamical systems and their embeddings from data. We consider two canonical cases: (i) systems for which we have full measurements of the governing variables and (ii) systems for which we have incomplete measurements. For systems with full state measurements, we show that the recent sparse identification of nonlinear dynamical systems (SINDy) method can discover governing equations with relatively little data, provided that accurate measurements of the derivatives can be computed from the data. We introduce a sampling method that allows SINDy to scale efficiently to problems with multiple time scales; specifically, we can discover distinct governing equations at slow and fast scales. For systems with incomplete observations, we show that the Hankel alternative view of Koopman (HAVOK) method, based on time-delay embedding coordinates, can be used to obtain a linear model and Koopman invariant measurement system that nearly perfectly captures the dynamics of nonlinear quasiperiodic systems on the attractor. We introduce two strategies for using HAVOK on systems with multiple time scales. Together, our approaches provide a suite of mathematical strategies for reducing the data required to discover and model nonlinear multiscale systems.

Kathleen P. Champion

Steven L. Brunton

J. Nathan Kutz

SIAM J. Appl. Dyn. Syst.

Discovery of Nonlinear Multiscale Systems: Sampling Strategies and Embeddings

非线性多尺度系统发现：采样策略与嵌入方法

Dimitrios G. Patsatzis

Lucia Russo

Constantinos Siettos

Slow Invariant Manifolds of Fast-Slow Systems of ODEs with Physics-Informed Neural Networks

具有物理信息神经网络的常微分方程快慢系统的慢不变流形

Alberto Padovan

Blaine Vollmer

Daniel J. Bodony

Data-Driven Model Reduction via Non-intrusive Optimization of Projection Operators and Reduced-Order Dynamics

通过非侵入式优化投影算子和简化动力学的数据驱动模型降阶

Isam Al-Darabsah

Sue Ann Campbell

Bootan Rahman

Distributed Delay and Desynchronization in a Neural Mass Model

神经质量模型中的分布延迟与去同步化

Paweł Dłotko

Michał Lipiński

Justyna Signerska-Rynkowska

Testing Topological Conjugacy of Time Series

测试时间序列的拓扑共轭性

Katherine J. Meyer

Horace Fusco

Collin Smith

Alanna Hoyer-Leitzel

Continuation of Fixed Points and Bifurcations from ODE to Flow-Kick Disturbance Models

从常微分方程到流-踢扰动模型的不动点延续与分岔

短名	SIAM J. Appl. Dyn. Syst.
Journal Impact	1.79
国际分区	PHYSICS, MATHEMATICAL(Q2)
期刊索引	SCI Q1中科院 4 区

ISSN	1536-0040
h-index	67
国内分区	数学(4区)数学物理数学物理(3区)数学应用数学(4区)

涉及主题	数学物理计算机科学量子力学数学分析工程类人工智能非线性系统经济几何学应用数学统计物理学生物纯数学管理分叉
出版信息	出版商: Society for Industrial and Applied Mathematics Publications，出版周期: Quarterly，期刊类型: journal，开源期刊: 否
基本数据	创刊年份: 2002，原创研究文献占比: 100.00%，自引率:5.90%， Gold OA占比: 1.12%
平均审稿周期	网友分享经验：较慢,6-12周
平均录用比例	网友分享经验：容易

SIAM Journal on Applied Dynamical Systems

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