Physica D: Nonlinear Phenomena最新文献

英文中文

On some elliptic generalizations of the Metropolis–Stein–Stein map Metropolis-Stein-Stein映射的一些椭圆推广

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-11-13 DOI: 10.1016/j.physd.2025.135036

Ricardo Chacón , Pedro J. Martínez

Jacobian elliptic functions have been at the heart of nonlinear science for two hundred years. Through the exploration of two biparametric (

λ, m

) elliptic-based generalizations of the Metropolis–Stein–Stein (MSS) map,

x_{n + 1} = f_{sn} (x_{n})

and

x_{n + 1} = f_{sn cn} (x_{n})

, with

sn

and

cn

being Jacobian elliptic functions of parameter

m

, we provide analytical and numerical evidence that solely varying the impulse per unit of amplitude of the periodic map functions, while keeping its amplitude

λ

constant, shifts the bifurcation amplitudes, including those corresponding to the onset and extinction of chaos, with respect to the case of the standard MSS map. The analyses of the Schwarzian derivative of the two elliptic maps indicate that a change of its sign from negative to positive as the shape parameter

m

is increased from 0 to 1 only occurs for the map

f_{sn cn}

, while the corresponding routes order

\leftrightarrow

chaos for both elliptic maps still follow Feigenbaum’s universality. We found that maximal extension of the state space wherein

f_{sn cn}

presents a positive Schwarzian derivative occurs at a single critical value of the shape parameter:

m = m_{c} ≃ 0.985682

. Remarkably, this value corresponds to a magic universal waveform which optimally enhances directed ratchet transport by symmetry breaking and is associated with an enhancement of chaos for

m ≲ 1

in parameter space with respect to the shift-symmetric map

f_{sn}

It should be emphasized that this change in the sign of the Schwarzian derivative is a genuine feature of the map

f_{sn cn}

which is completely absent in the standard MSS map.

雅可比椭圆函数是近两百年来非线性科学的核心。通过探索两个双参数（λ,m）椭圆型的Metropolis-Stein-Stein （MSS）映射，xn+1=fsn（xn）和xn+1=fsncn(xn)，其中sn和cn为参数m的雅可比椭圆函数，我们提供了解析和数值证据，证明在保持其振幅λ恒定的情况下，仅改变周期映射函数的单位振幅脉冲，可以改变分岔幅值，包括混沌开始和消失对应的分岔幅值。相对于标准MSS地图的情况。对两个椭圆映射的Schwarzian导数的分析表明，当形状参数m从0增加到1时，其符号从负到正的变化只发生在映射fsncn上，而两个椭圆映射的相应路由顺序↔混沌仍然遵循Feigenbaum的普适性。我们发现fsncn呈现正Schwarzian导数的状态空间的最大扩展出现在形状参数的一个临界值m=mc≃0.985682处。值得注意的是，该值对应于一个神奇的通用波形，该波形通过对称破缺优化地增强了有向棘轮传输，并且与参数空间中相对于移位对称映射fsn的m > 1的混沌增强有关。应该强调的是，Schwarzian导数符号的这种变化是映射fsncn的真正特征，这在标准MSS映射中是完全不存在的。

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引用次数: 0

Dynamics analysis of a tri-neuron discrete-time BAM neural network with two delays 具有两个时滞的三神经元离散BAM神经网络的动力学分析

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-11-13 DOI: 10.1016/j.physd.2025.135035

Lianjie Song, Wei Liang, Qiu Du

A tri-neuron discrete-time BAM neural network with two delays is considered in this paper. When the network satisfies several relatively weak conditions, one criterion of stability is established. Moreover, proof of the existence of chaos in the sense of Li–Yorke and Devaney is given by applying the snap-back repeller theory. One example is demonstrated by showing its chaotic behavior and the trends of the largest Lyapunov exponent, which further illustrates the correctness of the obtained results.

研究了一种具有两个时滞的三神经元离散时间BAM神经网络。当网络满足几个相对较弱的条件时，建立一个稳定性判据。此外，利用回跳排斥理论证明了Li-Yorke和Devaney意义上混沌的存在性。通过一个例子，给出了其混沌行为和最大Lyapunov指数的变化趋势，进一步说明了所得结果的正确性。

引用次数: 0

Optimization of dynamics indicators in pendular systems 摆式系统动力学指标的优化

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-11-12 DOI: 10.1016/j.physd.2025.135028

Daniel Pérez-Palau , Diego Enrique Pico-Lache

Lyapunov exponents have been utilized extensively in the detection of chaos and stability. Various alternatives, such as finite-time Lyapunov exponents and Lagrangian descriptors, have been recently proposed with the objective of reducing the computational demands of the former. In this study, we introduce a novel indicator inspired by the Lagrangian descriptors for discrete systems. This approach facilitates the exploration and detection of chaos in pendular systems through the discretization of the system using Poincaré sections. A comparison of the results obtained with those from the literature was conducted, yielding successful outcomes. A drawback of those indicators is its high computational burden. An optimization procedure has been successfully implemented. This algorithm reduces the computational time by a factor up to 20 for some indicators. This new procedure outputs favourable results for those indicators that explore large system times.

李雅普诺夫指数在混沌和稳定性的检测中得到了广泛的应用。最近提出了各种替代方法，如有限时间李雅普诺夫指数和拉格朗日描述符，目的是减少前者的计算需求。在本研究中，我们引入了一个受离散系统拉格朗日描述符启发的新指标。这种方法通过使用庞卡罗剖面对系统进行离散化，便于对摆系统中的混沌进行探索和检测。将获得的结果与文献中的结果进行了比较，得出了成功的结果。这些指标的一个缺点是计算量大。一个优化程序已成功实现。该算法将某些指标的计算时间减少了20倍。这个新程序为那些探索大系统时间的指标提供了有利的结果。

引用次数: 0

Magnus exponential integrators for stiff time-varying stochastic systems 刚性时变随机系统的Magnus指数积分器

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-11-11 DOI: 10.1016/j.physd.2025.135034

Dev Jasuja , P.J. Atzberger

We introduce exponential numerical integration methods for handling stiff stochastic dynamical systems having time-varying dissipative operators and fluctuations. Time-dependence presents challenges for exponentiation to obtain tractable expressions for evaluation, especially when the dissipative operators do not commute in time. We introduce approaches based on statistical mechanics and Magnus expansions to obtain stochastic integration methods that exhibit fluctuation–dissipation balance and other properties that facilitate computations. We show how practical computational methods can be developed to approximate and evaluate the contributions of the resulting stochastic expressions. We demonstrate our methods on several examples, including time-varying SDEs that arise in particle simulations and for SPDEs that model fluctuations in concentration fields of spatially-extended systems. Our introduced approaches provide methods for preserving statistical structures and other properties to obtain exponential numerical integrators for handling stiffness in time-varying stochastic dynamical systems.

本文引入指数数值积分方法来处理具有时变耗散算子和波动的刚性随机动力系统。当耗散算子不随时间交换时，时间依赖性给幂运算获得易于处理的求值表达式带来了挑战。我们引入了基于统计力学和Magnus展开的方法来获得具有波动-耗散平衡和其他便于计算的特性的随机积分方法。我们展示了如何开发实用的计算方法来近似和评估所得随机表达式的贡献。我们在几个例子上展示了我们的方法，包括在粒子模拟中出现的时变SDEs和在空间扩展系统的浓度场中模拟波动的SPDEs。我们介绍的方法提供了保留统计结构和其他性质的方法，以获得指数数值积分器，用于处理时变随机动力系统的刚度。

引用次数: 0

Long-time asymptotic behavior of the generalized coupled high-order nonlinear Schrödinger equation with solitons 具有孤子的高阶广义耦合非线性Schrödinger方程的长时间渐近行为

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-11-11 DOI: 10.1016/j.physd.2025.135017

Wenxia Chen , Chaosheng Zhang , Boling Guo , Lixin Tian

In this paper, we address the long-time asymptotic behavior of the generalized coupled high-order nonlinear Schrödinger (gCH-NLS) equation with initial data in Schwartz space

S (R)

that can support solitons. We construct the corresponding Riemann–Hilbert (RH) problem based on the spectral analysis of the associated 3 × 3 matrix Lax pair. By eliminating discrete spectral singularities through the Darboux transformation, we transform the original RH problem into a new RH problem without poles. Employing the nonlinear steepest-descent method for RH problems, as introduced by Deift and Zhou, we derive the long-time asymptotic expansion of the solution

q (x, t)

, achieving a residual error on the order of

O (t^{- \frac{3}{4} + \frac{1}{2 p}})

, where

2 \leq p < \infty

. Notably, our results can directly derive the long-time asymptotic behavior with soliton of both the fourth-order dispersive nonlinear Schrödinger equation and the coupled high-order nonlinear Schrödinger systems as special cases.

本文研究了具有初始数据的Schwartz空间中支持孤子的广义耦合高阶非线性Schrödinger （gCH-NLS）方程的长时间渐近性质。基于相关的3 × 3矩阵Lax对的谱分析，构造了相应的Riemann-Hilbert （RH）问题。通过Darboux变换消除离散谱奇点，将原RH问题转化为无极点的新RH问题。利用Deift和Zhou引入的RH问题的非线性最陡下降法，我们导出了解q（x,t）的长时间渐近展开，得到了O（t−34+12p）阶的残差，其中2≤p<；∞。值得注意的是，我们的结果可以直接导出四阶色散非线性Schrödinger方程和耦合高阶非线性Schrödinger系统作为特例的长时间渐近孤子行为。

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引用次数: 0

Controllable spatial bifurcation in optomechanical system: Analytical and numerical study 光力学系统中的可控空间分岔：解析与数值研究

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-11-11 DOI: 10.1016/j.physd.2025.134982

Elizaveta Soboleva, Semyon Rudyi, Dmitrii Shcherbinin, Andrei Ivanov

We propose an optomechanical system that can be used as a platform for an Ising machine featuring controllable spatial bifurcation. The system is based on a hybrid surface trap for charged particles, consisting of a planar electrode structure and a laser beam directed perpendicular to the electrode surface. This configuration exhibits bistable dynamics with a pitchfork-type bifurcation between stable particle localization points. We establish the functional dependence of bifurcation parameter on physical system parameters, including electrode geometry, electrodynamic field characteristics, particle properties, and laser power. The system dynamics is analyzed in two scenarios: under compensation of optical radiation pressure and gravitational forces, and without such compensation. Bifurcation control is achieved by tuning the laser intensity. A one-dimensional effective potential model of the system has been described in terms of Duffing potential.

我们提出了一个光机械系统，它可以作为一个具有可控空间分岔的伊辛机的平台。该系统基于带电粒子的混合表面陷阱，由平面电极结构和垂直于电极表面的激光束组成。这种结构表现出双稳态动力学，在稳定粒子局部化点之间具有干草叉型分岔。我们建立了分岔参数与物理系统参数的函数依赖关系，包括电极几何形状、电动力场特性、粒子特性和激光功率。分析了有光辐射、压力和重力补偿和无补偿两种情况下的系统动力学特性。分岔控制是通过调节激光强度来实现的。用Duffing势描述了系统的一维有效势模型。

引用次数: 0

Data driven neural network approaches for pricing options 定价期权的数据驱动神经网络方法

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-11-11 DOI: 10.1016/j.physd.2025.134992

Samuel M. Nuugulu , Kailash C. Patidar , Divine T. Tarla

This paper presents two data driven approaches, the purely data driven (PDD) and physics informed neural network (PINN) approach for solving asset pricing problems. The PDD approach relies purely on available data and does not require any governing partial differential equation (PDE) to solve a pricing problem. On the other hand, under the PINN approach, the pricing is done by solving a governing PDE. Both models are calibrated to observed market prices, and their implied volatilities are compared to those derived from market data and the classical Black–Scholes model. The absolute errors and maximum absolute errors metrics relative to observed implied volatilities and prices and the prices obtained from the classical Black–Scholes model were used in measuring the goodness-of-fit of the two proposed techniques. Several hyperparameter tuning techniques were employed to optimize the performance of the two methods. In addition, we analyze the probability density functions (PDFs) derived from each method and verify that they are valid by demonstrating positivity and proper normalization. Theoretical results, including propositions and theorems, are presented to establish conditions under which the PINN, trained using the Adam optimizer and initialized via the Xavier method, converges to an optimal solution, i.e., a set of trainable parameters that minimize the loss function. In further extensions, the PINN approach was applied to pricing European put options under a Heston stochastic volatility model (HSVM) model. While both methods exhibit competitive performance when calibrated, our empirical findings indicate that the PINN approach yields superior accuracy and stability.

本文提出了两种数据驱动方法，纯数据驱动（PDD）和物理通知神经网络（PINN）方法，用于解决资产定价问题。PDD方法完全依赖于可用数据，不需要任何控制偏微分方程（PDE）来解决定价问题。另一方面，在PINN方法下，定价是通过解决一个控制PDE来完成的。这两个模型都是根据观察到的市场价格进行校准的，并将其隐含波动率与来自市场数据和经典布莱克-斯科尔斯模型的隐含波动率进行比较。相对于观察到的隐含波动率和价格的绝对误差和最大绝对误差指标以及从经典布莱克-斯科尔斯模型获得的价格被用于测量两种提出的技术的拟合优度。采用了几种超参数调谐技术来优化两种方法的性能。此外，我们分析了每种方法的概率密度函数（pdf），并通过证明正性和适当的归一化来验证它们是有效的。给出了一些理论结果，包括命题和定理，以建立使用Adam优化器训练并通过Xavier方法初始化的PINN收敛到最优解的条件，即一组使损失函数最小的可训练参数。在进一步的扩展中，将PINN方法应用于Heston随机波动率模型（HSVM）模型下的欧洲看跌期权定价。虽然两种方法在校准时都表现出竞争力，但我们的实证研究结果表明，PINN方法具有更高的准确性和稳定性。

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引用次数: 0

On the propagation of regularity of solutions to the KdV equation on the positive half-line KdV方程解的正则性在正半线上的传播

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-11-10 DOI: 10.1016/j.physd.2025.135030

Márcio Cavalcante , Ailton C. Nascimento

We study special regularity properties of solutions to the initial–boundary value problem associated with the Korteweg–de Vries equations posed on the positive half-line. In particular, for initial data

u_{0} \in H^{{\frac{3}{4}}^{+}} (R^{+})

and boundary data

f \in H^{{\frac{3}{2}}^{+}} (R^{+})

, where the restriction of

u_{0}

to some subset of

(b, \infty)

has an extra regularity for any

b > 0

, we prove that the regularity of solutions

u

moves with infinite speed to its left as time evolves until a certain time

T^{*}

. The existence of a stopping time

T^{*}

appears because of the effect of the boundary function

f

. Also, as a consequence of our proof, we prove a gain in the regularity of the trace derivatives of the solutions for the Korteweg–de Vries on the half-line.

研究了正半线上Korteweg-de Vries方程初边值问题解的特殊正则性。特别地，对于初始数据u0∈H34+(R+)和边界数据f∈H32+(R+)，其中u0对（b,∞）的某个子集的限制对于任意b>；0具有额外的规律性，我们证明了解u的正则性随着时间的发展以无限的速度向左移动，直到某时刻T *。由于边界函数f的作用，出现了停止时间T *的存在性。同时，作为我们证明的结果，我们再次证明了半线上Korteweg-de Vries解的迹导数的正则性。

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引用次数: 0

Gravitational collapse of liquid layer cavities near boundaries 边界附近液层空腔的引力坍缩

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-11-10 DOI: 10.1016/j.physd.2025.135032

R. Camassa , G. Falqui , G. Ortenzi , M. Pedroni

Collapse of a cavity, or a depression hollow, in a water layer under gravity is modeled with the so-called Shallow Water equations in three dimensional settings, under circular symmetry and its deformation to elliptical cross sections. Self-similar, explicit solutions are found by quadratures in terms of elliptic integrals. We show that the presence of a rigid floor and the proximity of the cavity to this boundary significantly affects the evolution of the free surface, with the collapse evolving to form jet pairs originating at the caustics locations determined by the initial ellipsoidal cavity. The loss of symmetry implied by the deformation to elliptical cross sectional shapes leads to time evolution governed by an integrable two-degree of freedom Hamiltonian system. It is shown that the formation of the singularities is a reflection of the different critical exponents of the fluid velocity components in the solutions, with only the component aligned with the minor axis exhibiting a gradient catastrophe in finite time.

在重力作用下，水层中的空腔或凹陷的塌陷是用所谓的三维浅水方程来模拟的，在圆形对称和椭圆截面的变形下。自相似的显式解由椭圆积分的正交得到。我们表明，刚性底板的存在和靠近该边界的空腔显著影响自由表面的演变，随着坍塌演变成射流对，它们起源于由初始椭球形空腔确定的焦散位置。椭圆截面形状的变形所导致的对称性损失导致了由可积的二自由度哈密顿系统控制的时间演化。结果表明，奇异点的形成是溶液中流体速度分量的不同临界指数的反映，只有与小轴对齐的分量在有限时间内呈现梯度突变。

引用次数: 0

A robust ensemble time-localization H-infinity filter for chaotic dynamical models 混沌动力学模型的鲁棒集合时间局部化h∞滤波器

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-11-10 DOI: 10.1016/j.physd.2025.135033

Ruixiang Jia, Yulong Bai, Wenbin Yue, Xiaoxin Yue

Enhancing the robustness and accuracy of data assimilation (DA) systems is crucial for reliable state estimation in high-dimensional, nonlinear dynamical environments, where classical ensemble-based approaches often suffer from spurious long-range correlations and limited adaptability to multiscale dynamics. To address these challenges, this study introduces EnTLHF-RL, an improved filtering framework that incorporates spatial localization into the Ensemble Time-Localized H∞ Filter (EnTLHF). The proposed approach employs a correlation-based localization matrix to attenuate cross-variable correlations induced by finite-ensemble effects, while simultaneously introducing dynamic observation error estimation and quality control, thereby reinforcing spatial locality, enhancing numerical stability, and strengthening the overall reliability and adaptability of the assimilation framework. This design improves both the robustness and adaptability of the filter in regimes characterized by strong nonlinearity and chaotic behavior. The method is evaluated using Observing System Simulation Experiments (OSSEs) on two representative benchmark models: the Lorenz-96 system, under varying levels of dynamical forcing, and the Kuramoto–Sivashinsky (KS) equation, which exemplifies high-dimensional spatiotemporal chaos. Across both systems, EnTLHF-RL demonstrates superior performance over Ensemble Kalman Filter (EnKF) and EnTLHF, yielding lower root mean square errors and improved long-term stability. These results highlight the method’s potential as a robust and scalable assimilation framework for nonlinear physical systems under uncertainty.

提高数据同化（DA）系统的鲁棒性和准确性对于高维非线性动态环境中可靠的状态估计至关重要，在这些环境中，经典的基于集成的方法往往存在虚假的远程相关性和对多尺度动态的有限适应性。为了解决这些挑战，本研究引入了EnTLHF- rl，这是一种改进的滤波框架，将空间定位融入到集成时间本地化H∞滤波器（EnTLHF）中。该方法采用基于相关性的定位矩阵来减弱有限系综效应引起的交叉变量相关性，同时引入动态观测误差估计和质量控制，从而增强同化框架的空间局域性，增强数值稳定性，增强同化框架的整体可靠性和适应性。这种设计提高了滤波器在强非线性和混沌状态下的鲁棒性和自适应性。利用观测系统仿真实验（OSSEs）对Lorenz-96系统和Kuramoto-Sivashinsky （KS）方程这两个具有代表性的基准模型进行了评估，其中Lorenz-96系统具有不同的动力强迫水平，Kuramoto-Sivashinsky （KS）方程体现了高维时空混沌。在这两个系统中，EnTLHF- rl表现出优于集成卡尔曼滤波器（EnKF）和EnTLHF的性能，产生更低的均方根误差，并提高了长期稳定性。这些结果突出了该方法作为不确定性下非线性物理系统的鲁棒和可扩展同化框架的潜力。

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