Physica D: Nonlinear Phenomena最新文献

英文中文

The dynamic of the positons for the reverse space–time nonlocal short pulse equation 反向时空非局域短脉冲方程的正子动态

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2024-11-14 DOI: 10.1016/j.physd.2024.134419

Jiaqing Shan, Maohua Li

In this paper, the Darboux transformation (DT) of the reverse space–time (RST) nonlocal short pulse equation is constructed by a hodograph transformation and the eigenfunctions of its Lax pair. The multi-soliton solutions of the RST nonlocal short pulse equation are produced through the DT, which can be expressed in terms of determinant representation. The correctness of DT and determinant representation of N-soliton solutions are proven. By taking different values of eigenvalues, bounded soliton solutions and unbounded soliton solutions can be obtained. In addition, based on the degenerate Darboux transformation, the

N

-positon solutions of the RST nonlocal short pulse equation are computed from the determinant expression of the multi-soliton solution. The decomposition of positons, approximate trajectory and “phase shift” after collision are discussed explicitly. Furthermore, different kinds of mixed solutions are also presented, and the interaction properties between positons and solitons are investigated.

本文通过霍多图变换及其拉克斯对的特征函数，构建了反向时空（RST）非局域短脉冲方程的达布变换（Darboux transformation，DT）。通过 DT 生成 RST 非局部短脉冲方程的多孑子解，可以用行列式表示。证明了 DT 和行列式表示 N 玻利子解的正确性。通过取不同的特征值，可以得到有界孤子解和无界孤子解。此外，基于退化达尔布变换，从多孤子解的行列式表达计算出 RST 非局部短脉冲方程的 N 正子解。明确讨论了正子分解、近似轨迹和碰撞后的 "相移"。此外，还提出了不同种类的混合解，并研究了正子和孤子之间的相互作用特性。

引用次数: 0

Symmetric comet-type periodic orbits in the elliptic three-dimensional restricted (N+1)-body problem 椭圆三维受限 (N+1)- 体问题中的对称彗星型周期轨道

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2024-11-12 DOI: 10.1016/j.physd.2024.134426

Josep M. Cors , Miguel Garrido

For

N \geq 3

, we show the existence of symmetric periodic orbits of very large radii in the elliptic three-dimensional restricted

(N + 1)

-body problem when the

N

primaries have equal masses and are arranged in a

N

-gon central configuration. These periodic orbits are close to very large circular Keplerian orbits lying nearly a plane perpendicular to that of the primaries. They exist for a discrete sequence of values of the mean motion, no matter the value of the eccentricity of the primaries.

对于 N≥3，我们证明了在椭圆形三维受限 (N+1)- 体问题中，当 N 个基体质量相等并以 N 宫中心构型排列时，存在半径非常大的对称周期轨道。这些周期轨道接近于非常大的圆形开普勒轨道，几乎位于垂直于基体的平面上。无论主星的偏心率是多少，它们都存在于平均运动的离散值序列中。

引用次数: 0

Jensen-autocorrelation function for weakly stationary processes and applications 弱静止过程的詹森自相关函数及其应用

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2024-11-07 DOI: 10.1016/j.physd.2024.134424

Javier E. Contreras-Reyes

The Jensen-variance (JV) information based on Jensen’s inequality and variance has been previously proposed to measure the distance between two random variables. Based on the relationship between JV distance and autocorrelation function of two weakly stationary process, the Jensen-autocovariance and Jensen-autocorrelation functions are proposed in this paper. Furthermore, the distance between two different weakly stationary processes is measured by the Jensen-cross-correlation function. Moreover, autocorrelation function is also considered for ARMA and ARFIMA processes, deriving explicit formulas for Jensen-autocorrelation function that only depends on model parametric space and lag, whose were also illustrated by numeric results. In order to study the usefulness of proposed functions, two real-life applications were considered: the Tree Ring and Southern Humboldt current ecosystem time series.

以前曾提出过基于詹森不等式和方差的詹森方差（JV）信息来测量两个随机变量之间的距离。根据 JV 距离与两个弱静止过程的自相关函数之间的关系，本文提出了 Jensen-自方差函数和 Jensen-自相关函数。此外，两个不同弱静止过程之间的距离用詹森-交叉相关函数来衡量。此外，还考虑了 ARMA 和 ARFIMA 过程的自相关函数，推导出了仅取决于模型参数空间和滞后期的詹森-自相关函数的明确公式，并通过数值结果对其进行了说明。为了研究拟议函数的实用性，考虑了两个实际应用：树环和南洪堡海流生态系统时间序列。

引用次数: 0

About the chaos influence on a system with multi-frequency quasi-periodicity and the Landau-Hopf scenario 关于混沌对多频准周期性系统的影响以及 Landau-Hopf 情景

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2024-11-06 DOI: 10.1016/j.physd.2024.134425

A.P. Kuznetsov, L.V. Turukina

The interaction of system demonstrating multi-frequency quasi-periodic oscillations and several steps of the Landau-Hopf scenario with chaotic Rössler system is considered. The quasi-periodic subsystem is a network of five non-identical van der Pol oscillators. It is shown that as the coupling parameter between the subsystems decreases, successive quasi-periodic Hopf bifurcations and doublings of high-dimensional invariant tori are observed. The chaos arising in this system can have several (in our case up to five) additional zero Lyapunov exponents. In case of weak coupling parameter between chaotic and quasi-periodic subsystems, when the coupling parameter of van der Pol oscillators changes, the points at which the attractor transformation occurs are observed. This is a new type of bifurcations that are responsible for a consistent increase in the number of additional zero Lyapunov exponents. As the coupling parameter between chaotic and quasi-periodic subsystems increases, the observed stages of the Landau-Hopf scenario turns out to be resistant to interaction with the chaotic system.

研究考虑了显示多频率准周期振荡和兰道-霍普夫情景几个步骤的系统与混沌罗斯勒系统的相互作用。准周期子系统是由五个非同范德尔波尔振荡器组成的网络。研究表明，随着子系统之间耦合参数的减小，会观察到连续的准周期霍普夫分岔和高维不变环的加倍。在这个系统中产生的混沌可能有几个（在我们的例子中最多有五个）额外的零 Lyapunov 指数。在混沌子系统和准周期子系统之间存在弱耦合参数的情况下，当范德尔波尔振荡器的耦合参数发生变化时，就会观察到吸引子转换发生的点。这是一种新型分岔，是额外零 Lyapunov 指数数量持续增加的原因。随着混沌子系统和准周期子系统之间耦合参数的增加，观察到的朗道-霍普夫情景阶段原来可以抵抗与混沌系统的相互作用。

引用次数: 0

Soliton resolution for the Ostrovsky–Vakhnenko equation 奥斯特洛夫斯基-瓦赫年科方程的孤子解析

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2024-11-04 DOI: 10.1016/j.physd.2024.134416

Ruihong Ma, Engui Fan

We consider the Cauchy problem of the Ostrovsky–Vakhnenko (OV) equation expressed in the new variables

(y, τ)

q^{3} - q {(log q)}_{y τ} - 1 = 0

with Schwartz initial data

q_{0} (y) > 0

which supports smooth and single-valued solitons. It is shown that the solution to the Cauchy problem for the OV equation can be characterized by a 3 × 3 matrix Riemann–Hilbert (RH) problem. Furthermore, by employing the

\bar{\partial}

-steepest descent method to deform the RH problem into solvable models, we derive the soliton resolution for the OV equation across two space–time regions:

y / τ > 0

and

y / τ < 0

. This result also implies that the

N

-soliton solutions of the OV equation in variables

(y, τ)

are asymptotically stable.

我们考虑的是以新变量 (y,τ) q3-q(logq)yτ-1=0 表示的奥斯特洛夫斯基-瓦赫年科方程（OV）的考奇问题，其初始数据为施瓦茨 q0(y)>0，支持光滑的单值孤子。研究表明，OV 方程的考奇问题解可以用一个 3 × 3 矩阵黎曼-希尔伯特（RH）问题来表征。此外，通过使用 ∂̄-steepest descent 方法将 RH 问题变形为可解模型，我们推导出了 OV 方程在两个时空区域的孤子分辨率：y/τ>0 和 y/τ<0。这一结果还意味着，OV方程在变量（y,τ）中的N个孤子解是渐近稳定的。

引用次数: 0

Global dynamics of a periodically forced SI disease model of Lotka–Volterra type 洛特卡-沃尔特拉型周期性强迫 SI 疾病模型的全局动力学

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2024-11-04 DOI: 10.1016/j.physd.2024.134422

Yuheng Song , Lei Niu

In this paper, we investigate the dynamics of an SI disease model of Lotka–Volterra type in the presence of a periodically fluctuating environment. We give a global analysis of the dynamical behavior of the model. Interestingly, our results show that the permanence guarantees the existence of a unique positive harmonic time-periodic solution which is globally attracting when the horizontal disease transmission has a weaker impact than the intraspecific competition. While for the case when the horizontal disease transmission has a stronger impact than the intraspecific competition, we numerically show that complex dynamics such as chaos can occur in a permanent system. Nonetheless, we provide sufficient conditions for the existence and uniqueness of the positive harmonic time-periodic solution for the latter case. The impact of the environment on the spread of disease is studied by using a bifurcation analysis. We show that in each of the qualitatively different cases of the associated autonomous SI model in a constant environment, an alternative possibility can appear in the periodic model.

在本文中，我们研究了一个洛特卡-伏特拉（Lotka-Volterra）类型的 SI 疾病模型在周期性波动环境下的动力学。我们对模型的动力学行为进行了全局分析。有趣的是，我们的结果表明，当疾病的水平传播比种内竞争的影响弱时，永恒性保证了唯一的正谐波时间周期解的存在，该解具有全局吸引力。而当疾病水平传播的影响强于种内竞争的影响时，我们的数值结果表明，在永久系统中会出现复杂的动态变化，如混乱。尽管如此，我们还是为后一种情况下正谐波时间周期解的存在性和唯一性提供了充分条件。我们通过分岔分析研究了环境对疾病传播的影响。我们表明，在恒定环境中的相关自主 SI 模型的每一种质的不同情况下，周期模型中都可能出现另一种可能性。

引用次数: 0

Chaotic fields out of equilibrium are observable independent 失去平衡的混沌场是独立可观测的

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2024-11-04 DOI: 10.1016/j.physd.2024.134421

D. Lippolis

Chaotic dynamics is always characterized by swarms of unstable trajectories, unpredictable individually, and thus generally studied statistically. It is often the case that such phase-space densities relax exponentially fast to a limiting distribution, that rules the long-time average of every observable of interest. Before that asymptotic time scale, the statistics of chaos is generally believed to depend on both the initial conditions and the chosen observable. I show that this is not the case for a widely applicable class of models, that feature a phase-space (‘field’) distribution common to all pushed-forward or integrated observables, while the system is still relaxing towards statistical equilibrium or a stationary state. This universal profile is determined by both leading and first subleading eigenfunctions of the transport operator (Koopman or Perron–Frobenius) that maps phase-space densities forward or backward in time.

混沌动力学总是以不稳定的轨迹群为特征，无法单独预测，因此一般采用统计学方法进行研究。通常情况下，这种相空间密度会以指数级的速度松弛到一个极限分布，即每个相关观测指标的长期平均值。一般认为，在渐近时间尺度之前，混沌统计取决于初始条件和所选观测指标。我的研究表明，对于一类广泛应用的模型来说，情况并非如此，这类模型的特点是，当系统仍在向统计平衡或静止状态松弛时，所有前推或综合观测值都有一个共同的相空间（"场"）分布。这种普遍分布是由传输算子（Koopman 或 Perron-Frobenius）的前导和第一副导特征函数决定的，而传输算子可以在时间上向前或向后映射相空间密度。

引用次数: 0

Jacobi stability, Hamilton energy and the route to hidden attractors in the 3D Jerk systems with unique Lyapunov stable equilibrium 具有唯一李雅普诺夫稳定均衡的三维 Jerk 系统中的雅可比稳定性、汉密尔顿能量和通向隐藏吸引子的路径

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2024-11-04 DOI: 10.1016/j.physd.2024.134423

Xiaoting Lu, Qigui Yang

This paper is devoted to reveal the generation mechanism of hidden attractors of the 3D Jerk systems with unique Lyapunov stable equilibrium. In the light of the deviation curvature tensor, the two-parameter regions with Lyapunov stable but Jacobi unstable equilibrium are identified. Within these regions, the system’s dynamics transition from Lyapunov stable but Jacobi unstable equilibrium to hidden periodic and then to hidden chaotic attractors, which the corresponding Hamilton energy tend to be constant, regular and irregular oscillations, respectively. The route to hidden attractors of the systems with Jacobi unstable equilibrium is analyzed under one parameter variation. The results show that the systems initially undergo a subcritical Hopf bifurcation, resulting in a Lyapunov unstable limit cycle, followed by a saddle–node bifurcation of limit cycle, ultimately entering hidden chaotic attractors via the Feigenbaum period-doubling route.

本文致力于揭示具有唯一 Lyapunov 稳定均衡的三维 Jerk 系统的隐性吸引子的生成机制。根据偏差曲率张量，确定了具有 Lyapunov 稳定但 Jacobi 不稳定均衡的双参数区域。在这些区域内，系统动力学从 Lyapunov 稳定但 Jacobi 不稳定平衡过渡到隐含周期吸引子，再过渡到隐含混沌吸引子，其对应的 Hamilton 能量分别趋向于恒定、规则和不规则振荡。分析了雅可比不稳定平衡系统在一个参数变化下通向隐性吸引子的路径。结果表明，系统最初经历了次临界霍普夫分岔，形成了一个莱普诺夫不稳定极限周期，随后又经历了极限周期的鞍节点分岔，最终通过费根鲍姆周期加倍路线进入隐性混沌吸引子。

引用次数: 0

Formal solutions of some family of inhomogeneous nonlinear partial differential equations, Part 2: Summability 某些非均质非线性偏微分方程族的形式解，第 2 部分：可求和性

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2024-11-01 DOI: 10.1016/j.physd.2024.134420

Alberto Lastra , Pascal Remy , Maria Suwińska

In this article, we investigate the summability of the formal power series solutions in time of a class of inhomogeneous nonlinear partial differential equations in two variables, whose corresponding Newton polygon admits a unique positive slope

k

, the latter being determined by the highest spatial-derivative order of the initial equation. We give in particular a necessary and sufficient condition for the

k

-summability of the solutions in a given direction, and we illustrate this result by some examples. This condition generalizes the ones already given by the second author in Remy (2016, 2020, 2021 [25,26], 2022, 2023). In addition, we present some technical results on the generalized binomial and multinomial coefficients, which are needed for the proof of our main result.

在本文中，我们研究了一类两变量非均质非线性偏微分方程的形式幂级数解的时间求和性，其相应的牛顿多边形具有唯一的正斜率 k，后者由初始方程的最高空间衍生阶决定。我们特别给出了在给定方向上解的 k 可求和性的必要条件和充分条件，并通过一些例子说明了这一结果。这个条件概括了第二作者在雷米（2016，2020，2021 [25,26]，2022，2023）中已经给出的条件。此外，我们还介绍了广义二项式系数和多项式系数的一些技术结果，这些结果是证明我们的主要结果所必需的。

引用次数: 0

To blow-up or not to blow-up for a granular kinetic equation 颗粒动力学方程的吹胀与否

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2024-10-28 DOI: 10.1016/j.physd.2024.134410

José A. Carrillo , Ruiwen Shu , Li Wang , Wuzhe Xu

A simplified kinetic description of rapid granular media leads to a nonlocal Vlasov-type equation with a convolution integral operator that is of the same form as the continuity equations for aggregation-diffusion macroscopic dynamics. While the singular behavior of these nonlinear continuity equations is well studied in the literature, the extension to the corresponding granular kinetic equation is highly nontrivial. The main question is whether the singularity formed in velocity direction will be enhanced or mitigated by the shear in phase space due to free transport. We present a preliminary study through a meticulous numerical investigation and heuristic arguments. We have numerically developed a structure-preserving method with adaptive mesh refinement that can effectively capture potential blow-up behavior in the solution for granular kinetic equations. We have analytically constructed a finite-time blow-up infinite mass solution and discussed how this can provide insights into the finite mass scenario.

对快速粒状介质的简化动力学描述导致了一个带有卷积积分算子的非局部 Vlasov 型方程，其形式与聚集-扩散宏观动力学的连续性方程相同。虽然这些非线性连续性方程的奇异行为在文献中得到了很好的研究，但扩展到相应的粒状动力学方程却非常不容易。主要的问题是，速度方向上形成的奇异性是否会因自由传输导致的相空间剪切而增强或减弱。我们通过细致的数值研究和启发式论证进行了初步研究。我们在数值上开发了一种自适应网格细化的结构保留方法，它能有效捕捉颗粒动力学方程求解中潜在的炸裂行为。我们从分析角度构建了有限时间炸毁的无限质量解，并讨论了该方法如何为有限质量情景提供启示。

引用次数: 0

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