Chaos, Solitons and Fractals: X最新文献

英文中文

A novel fitted mesh scheme involving Caputo–Fabrizio approach for singularly perturbed fractional-order differential equations with large negative shift 具有大负位移的奇摄动分数阶微分方程的一种新颖的Caputo-Fabrizio拟合网格格式

Q1 Mathematics

Chaos, Solitons and Fractals: X

Pub Date : 2025-12-01 Epub Date: 2025-02-13 DOI: 10.1016/j.csfx.2025.100128

Ababi Hailu Ejere, Tesfaye Tolu Feyissa

This study focuses on the formulation and analysis of a novel fitted mesh method for solving singularly perturbed time-fractional partial differential equations (SPTPDEs) with large negative shift. These equations pose significant challenges due to the combined effects of fractional-order derivative in time, small perturbation parameter, and negative shift term that lead to sharp boundary layers and potential numerical instability. In this work, the non-locality effect of the fractional–order is treated applying the Caputo–Fabrizio approach. The influence of the small perturbation parameter and large shift argument are controlled by formulating a fitted-mesh method utilizing the Crank–Nicolson approach in time and central difference method with Shishkin-type piece-wise uniform meshes in space. By these coupled techniques, the abruptly varying nature of the solution in the layer regions can be resolved effectively. We investigate and prove that the proposed numerical scheme is stable and convergent of order two in time, and order two with logarithmic factor in space. Numerical experiments are conducted to validate the theoretical findings and showcase the scheme’s efficiency and accuracy in handling the intricacies of the problem. The convergence analysis and numerical results show that the formulated scheme is a reliable tool to treat the considered class of time-fractional singularly perturbed differential equations consisting of large negative shift.

本文研究了求解具有大负位移的奇异摄动时间分数阶偏微分方程的一种新的拟合网格方法。由于时间上的分数阶导数、小扰动参数和负移项的综合影响，导致尖锐的边界层和潜在的数值不稳定性，这些方程提出了重大的挑战。本文应用Caputo-Fabrizio方法研究分数阶的非定域效应。在时间上采用Crank-Nicolson方法，在空间上采用shishkin型分段均匀网格，采用中心差分法，对小扰动参数和大位移参数的影响进行了控制。通过这些耦合技术，可以有效地解决层区域溶液的突然变化性质。我们研究并证明了所提出的数值格式在时间上是稳定的和二阶收敛的，在空间上是有对数因子的。数值实验验证了理论结果，并证明了该方案在处理复杂问题时的有效性和准确性。收敛性分析和数值结果表明，该格式是处理大负位移时分数阶奇摄动微分方程的可靠工具。

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引用次数: 0

Hopf and Turing bifurcations analysis for the modified Lengyel–Epstein system 改进的lengye - epstein系统的Hopf和Turing分岔分析

Q1 Mathematics

Chaos, Solitons and Fractals: X

Pub Date : 2025-06-01 Epub Date: 2025-02-03 DOI: 10.1016/j.csfx.2025.100127

Panpan Zhang , Jun Li , Kuilin Wu

In this paper, we investigate the dynamics for the modified Lengyel–Epstein system of the photosensitive CDIMA reaction. Specifically, considering the impact of illumination intensity, more limit cycles are discovered in the modified Lengyel–Epstein system compared to the original model. This enhancement not only enriches the dynamical phenomena but also indicates the system’s heightened sensitivity to the light intensity. By the center manifold theorem and normal form theory, we achieve the existence of Hopf bifurcation for both the corresponding ODE system and PDE system. Moreover, we provide some conditions for Turing instability, Turing bifurcation, spatially homogeneous and inhomogeneous Hopf bifurcation and Turing–Hopf bifurcation. Finally, we discuss the effect of illumination intensity for dynamical behavior of the modified Lengyel–Epstein system.

本文研究了光敏CDIMA反应的改进lengye - epstein体系的动力学。具体而言，考虑光照强度的影响，改进的lengyell - epstein系统比原模型发现了更多的极限环。这种增强不仅丰富了动力学现象，而且表明系统对光强的灵敏度提高。利用中心流形定理和范式理论，得到了相应的ODE系统和PDE系统的Hopf分岔的存在性。并且给出了图灵不稳定性、图灵分岔、空间齐次和非齐次Hopf分岔以及图灵- Hopf分岔的一些条件。最后讨论了光照强度对改进的lengye - epstein系统动力学行为的影响。

引用次数: 0

Enhanced scaling crossover detection in long-range correlated time series 长程相关时间序列的增强尺度交叉检测

Q1 Mathematics

Chaos, Solitons and Fractals: X

Pub Date : 2025-06-01 Epub Date: 2024-12-16 DOI: 10.1016/j.csfx.2024.100125

Yudai Fujimoto , Madhur Mangalam , Ken Kiyono

Various time series, such as biological signals and stock prices, exhibit long-range correlations and a fractal nature characterized by the power-law scaling in the low-frequency range of the power spectrum. Instead of the power spectral analysis, scaling analysis methods such as Detrended Fluctuation Analysis (DFA) and Detrending Moving-Average Analysis (DMA) have been employed to estimate the scaling exponent. Scaling analysis results often uncover crossover phenomena, highlighting two distinct scaling regions—a short- and a long-range exponent. Estimating the two respective scaling exponents and the crossover point is crucial, as they can provide insight into different underlying mechanisms or dynamics operating at various scales. However, DFA and DMA with higher-order detrending tend to distort the time scales, and methods for accurately estimating the crossover have not been thoroughly investigated. This study addresses scale distortions in higher-order DFA and DMA by leveraging the relationship between the fluctuation function and the power spectrum of time series. We propose a method for crossover estimation using the Savitzky–Golay differentiation filter. Applying this method to numerical experiments with an autoregressive process exhibiting crossovers demonstrated that our proposed technique estimates crossovers more accurately than conventional segmented regression approaches used in DFA and DMA. We applied the proposed scaling crossover estimation method to the time series of the postural center of pressure (CoP), showcasing its practical applications in studying long-range correlations in empirical time series.

各种时间序列，如生物信号和股票价格，表现出长期相关性和分形性质，其特征是功率谱低频范围内的幂律缩放。用非趋势波动分析（DFA）和非趋势移动平均分析（DMA）等标度分析方法代替功率谱分析来估计标度指数。标度分析结果经常揭示交叉现象，突出两个不同的标度区域-短期指数和长期指数。估计两个各自的缩放指数和交叉点是至关重要的，因为它们可以深入了解在不同尺度上运行的不同潜在机制或动态。然而，具有高阶去趋势的DFA和DMA往往会扭曲时间尺度，准确估计交叉的方法尚未得到充分研究。本研究利用波动函数与时间序列功率谱之间的关系来解决高阶DFA和DMA的尺度扭曲问题。我们提出了一种使用Savitzky-Golay微分滤波器的交叉估计方法。将该方法应用于显示交叉的自回归过程的数值实验表明，我们提出的技术比DFA和DMA中使用的传统分段回归方法更准确地估计交叉。将所提出的尺度交叉估计方法应用于体位压力中心（CoP）时间序列，展示了该方法在研究经验时间序列中远程相关性方面的实际应用。

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引用次数: 0

The boundary of Rauzy fractal and discrete tilings Rauzy分形与离散拼接的边界

Q1 Mathematics

Chaos, Solitons and Fractals: X

Pub Date : 2025-06-01 Epub Date: 2025-02-01 DOI: 10.1016/j.csfx.2025.100126

Hyosang Kang , Woojin Choi , Jeonghoon Rhee , Youchan Oh

We present two methods of constructing the Rauzy fractal by partitioning all points within it into disjoint sets, refer to as layers. We show how these layered structures of the Rauzy fractal can plot the boundary of the fractal effectively. By generalizing the self-replicating pattern of this structure, we demonstrate a new way of discrete tilings of two-dimensional plane.

我们提出了两种构造Rauzy分形的方法，将分形中的所有点划分为不相交的集合，称为层。我们展示了这些分层结构的Rauzy分形如何有效地绘制分形的边界。通过推广该结构的自复制模式，我们展示了一种二维平面离散铺层的新方法。

引用次数: 0

A high-order rogue wave generated by collision in three-component Bose–Einstein condensates 三组份玻色-爱因斯坦凝聚体碰撞产生的高阶流氓波

Q1 Mathematics

Chaos, Solitons and Fractals: X

Pub Date : 2024-12-01 Epub Date: 2024-08-22 DOI: 10.1016/j.csfx.2024.100120

Feilong He , Xiao-Dong Bai , Tiantian Li , Jin-Cui Zhao

The generation of high-order rogue waves (RWs) without the exact solution is an intriguing subject that has not yet been fully explored, especially for the third-order RWs. In this paper, we investigate the collision dynamics in a three-component Bose–Einstein condensate (BEC), and propose a scheme capable of generating such high-order RWs, such as second- and third-order RWs. The results show that the peaks of the three first-order RWs coincide in time and space when the third-order RWs are excited during the collision. Furthermore, by controlling the offsets of initial wavepackets and intraspecific interaction coefficients within the BEC, the collision behavior of RWs can be precisely manipulated. Compared to two-component BECs, these three-component collisions exhibit more diverse structures for exciting RW phenomena.

在没有精确解的情况下产生高阶无赖波（RWs）是一个有趣的课题，但尚未得到充分探索，尤其是三阶无赖波。本文研究了三分量玻色-爱因斯坦凝聚态（BEC）中的碰撞动力学，并提出了一种能够产生二阶和三阶无赖波等高阶无赖波的方案。结果表明，当三阶 RW 在碰撞过程中被激发时，三个一阶 RW 的峰值在时间和空间上是重合的。此外，通过控制初始波包的偏移和 BEC 内部的相互作用系数，可以精确地操纵 RW 的碰撞行为。与双组分 BEC 相比，这些三组分碰撞在激发 RW 现象方面表现出更多样化的结构。

引用次数: 0

Effects of synapse location, delay and background stochastic activity on synchronising hippocampal CA1 neurons 突触位置、延迟和背景随机活动对海马 CA1 神经元同步化的影响

Q1 Mathematics

Chaos, Solitons and Fractals: X

Pub Date : 2024-12-01 Epub Date: 2024-11-04 DOI: 10.1016/j.csfx.2024.100122

Alessandro Fiasconaro , Michele Migliore

We study the synchronisation of neurons in a realistic model under the Hodgkin–Huxley dynamics. To focus on the role of the different locations of the excitatory synapses, we use two identical neurons where the set of input signals is grouped at two different distances from the soma. The system is intended to represent a CA1 hippocampal neuron in which the synapses arriving from the CA3 neurons of the trisynaptic pathway appear to be localised in the apical dendritic region and are, in principle, either proximal or distal to the soma. Synchronisation is studied using a specifically defined spiking correlation function as a function of various parameters such as the distance from the soma of one of the synaptic groups, the inhibition weight and the associated activation delay. We found that the neurons’ spiking activity depends nonmonotonically on the relative dendritic location of the synapses and their inhibition weight, while the synchronisation measure always decreases with inhibition, and strongly depends on its activation time delay. In our model, the synaptic random subthreshold background activity substantially reduces synchronisation in a monotonic way, while highlights the importance of a balanced E/I contribution for neuronal synchronisation.

我们研究了霍奇金-赫胥黎动力学下神经元同步的现实模型。为了重点研究兴奋性突触的不同位置所起的作用，我们使用了两个相同的神经元，在这两个神经元中，一组输入信号被集中在离神经元体两个不同距离的地方。该系统旨在代表一个 CA1 海马神经元，在该神经元中，从三突触通路的 CA3 神经元到达的突触似乎位于顶端树突区域，原则上，这些突触要么靠近神经元体，要么远离神经元体。我们使用一个特定定义的尖峰相关函数来研究同步性，该函数是各种参数的函数，如其中一个突触群与神经元体的距离、抑制权重和相关激活延迟。我们发现，神经元的尖峰活动非单调地依赖于突触的相对树突位置及其抑制权重，而同步度量总是随着抑制而降低，并强烈依赖于其激活时间延迟。在我们的模型中，突触随机阈下背景活动以单调的方式大大降低了同步性，同时突出了均衡的 E/I 贡献对神经元同步性的重要性。

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引用次数: 0

Finite-time dynamics of the fractional-order epidemic model: Stability, synchronization, and simulations 分数阶流行病模型的有限时间动力学：稳定性、同步性和模拟

Q1 Mathematics

Chaos, Solitons and Fractals: X

Pub Date : 2024-12-01 Epub Date: 2024-07-15 DOI: 10.1016/j.csfx.2024.100118

Iqbal M. Batiha , Osama Ogilat , Issam Bendib , Adel Ouannas , Iqbal H. Jebril , Nidal Anakira

The aim of this paper is to explore finite-time synchronization in a specific subset of fractional-order epidemic reaction–diffusion systems. Initially, we introduce a new lemma for finite-time stability, which extends existing criteria and builds upon previous discoveries. Following this, we design effective state-dependent linear controllers. By utilizing a Lyapunov function, we derive new sufficient conditions to ensure finite-time synchronization within a predefined time frame. Lastly, we present numerical simulations to demonstrate the applicability and effectiveness of the proposed technique.

本文旨在探讨分数阶流行反应扩散系统特定子集中的有限时间同步性。首先，我们引入了一个新的有限时间稳定性(finite-time stability)lemma，该lemma扩展了现有的标准，并以之前的发现为基础。随后，我们设计了有效的与状态相关的线性控制器。通过利用 Lyapunov 函数，我们得出了新的充分条件，以确保在预定义的时间框架内实现有限时间同步。最后，我们通过数值模拟来证明所提技术的适用性和有效性。

引用次数: 0

Recurrence formula for some higher order evolution equations 一些高阶演化方程的递推公式

Q1 Mathematics

Chaos, Solitons and Fractals: X

Pub Date : 2024-12-01 Epub Date: 2024-07-20 DOI: 10.1016/j.csfx.2024.100119

Yoritaka Iwata

Riccati’s differential equation is formulated as abstract equation in finite or infinite dimensional Banach spaces. Since the Riccati’s differential equation with the Cole–Hopf transform shows a relation between the first order evolution equations and the second order evolution equations, its generalization suggests the existence of recurrence formula leading to a sequence of differential equations with different order. In conclusion, by means of the logarithmic representation of operators, a transform between the first order evolution equations and the higher order evolution equation is presented. Several classes of evolution equations with different orders are given, and some of them are shown as examples.

里卡提微分方程是有限维或无限维巴拿赫空间中的抽象方程。由于里卡提微分方程与科尔-霍普夫变换显示了一阶演化方程与二阶演化方程之间的关系，其广义化表明存在导致不同阶微分方程序列的递推公式。总之，通过算子的对数表示，提出了一阶演化方程与高阶演化方程之间的变换。给出了几类不同阶的演化方程，并以其中一些为例加以说明。

引用次数: 0

Solitary and traveling wave solutions to nematic liquid crystal equations using Jacobi elliptic functions 使用雅可比椭圆函数的向列液晶方程的孤波和行波解法

Q1 Mathematics

Chaos, Solitons and Fractals: X

Pub Date : 2024-12-01 Epub Date: 2024-09-18 DOI: 10.1016/j.csfx.2024.100121

Nikola Petrović , Milivoj Belić , Wieslaw Krolikowski

In our paper we apply the Jacobi elliptic function (JEF) expansion method to obtain exact solutions to the system of equations governing nematic liquid crystals, a system of high importance in nonlinear optics with numerous physical applications. We obtain solutions that are second-order polynomials in terms of JEFs for both the wave function and the tilt angle of molecular orientation. The solutions differ from previously obtained solutions in including both traveling and solitary wave solutions, with and without chirp. They also include the longitudinal dependence of coefficients in the equations, allowing for the management of both the dispersion and diffraction. Only two parameters of the differential equation need to be defined in terms of other coefficients, providing a wide range of flexibility when it comes to constructing solutions.

在我们的论文中，我们应用雅可比椭圆函数（JEF）展开法来获得向列液晶方程组的精确解，该方程组在非线性光学中具有重要意义，并有大量物理应用。我们得到的解是波函数和分子取向倾斜角的 JEF 二阶多项式。这些解与之前获得的解不同，既包括行波解，也包括孤波解，既有啁啾，也没有啁啾。它们还包括方程中系数的纵向依赖性，从而可以管理色散和衍射。微分方程中只有两个参数需要根据其他系数来定义，这为构建解法提供了广泛的灵活性。

引用次数: 0

From core to peripheral: A network analysis of lineup types in NBA playoff teams 从核心到边缘：NBA 季后赛球队阵容类型的网络分析

Q1 Mathematics

Chaos, Solitons and Fractals: X

Pub Date : 2024-12-01 Epub Date: 2024-06-06 DOI: 10.1016/j.csfx.2024.100115

Tianxiao Guo , Yixiong Cui , Christophe Ley , Wenjie Zhang , Yanfei Shen , Jing Mi , Chengyi Zhang

This study aims to identify the types of lineups based on their topological structure within a lineup network and to explore the relationship between lineup types and team standings during 10 NBA playoff seasons from 2012-2013 season to 2021-2022 season. A total of 15,699 lineups from 1,655 playoff games were collected to construct lineup networks. Three roles of the lineup, called core, connector and peripheral lineups, were found through community detection and unsupervised clustering of within-community degree, participation coefficient, and playing time. The percentage presence of connector lineups showed a positive correlation with the number of playoff wins (r = 0.45, p < 0.001), while peripheral lineups demonstrated a negative correlation (r = −0.33, p < 0.001). Additionally, the study found that connector lineups were more frequently reused than peripheral lineups (H = −14.90, p < 0.001) and that stronger teams exhibited lower conserved rates of all kinds of lineups. The collective performance was found to be more dependent on connector lineups (H = 926.42, p < 0.001) than peripheral lineups (H = 3342.63, p < 0.001). This study is the first to provide insights into the global lineup roles within season-scale lineup structures, offering generalizable suggestions for optimizing rotations. These suggestions advocate for the inclusion of more connector lineups and versatile players, and a reduction in the reuse rate of lineups, especially those classified as peripheral.

本研究旨在根据阵容网络中的拓扑结构识别阵容类型，并探讨从2012-2013赛季到2021-2022赛季的10个NBA季后赛赛季中阵容类型与球队排名之间的关系。研究共收集了 1,655 场季后赛中的 15,699 个阵容，构建了阵容网络。通过社群检测和对社群内程度、参与系数和上场时间的无监督聚类，发现了阵容的三种角色，即核心阵容、连接器阵容和外围阵容。连接器阵容出现的百分比与季后赛胜场数呈正相关（r = 0.45，p < 0.001），而外围阵容则呈负相关（r = -0.33，p < 0.001）。此外，研究还发现，连接器阵容比外围阵容更常被重用（H = -14.90，p <0.001），而强队的各种阵容的保留率更低。研究发现，与外围阵容（H = 3342.63，p <0.001）相比，集体表现更依赖于连接器阵容（H = 926.42，p <0.001）。本研究首次对赛季规模阵容结构中的整体阵容作用进行了深入分析，为优化轮换提供了可推广的建议。这些建议主张加入更多的连接器阵容和多面手，并降低阵容的重复利用率，尤其是那些被归类为边缘阵容的球员。

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