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Dynamics of a Random Hopfield Neural Lattice Model with Adaptive Synapses and Delayed Hebbian Learning 具有自适应突触和延迟海比学习的随机霍普菲尔德神经网格模型的动力学特性
IF 0.5 4区 数学 Q4 Mathematics
Ukrainian Mathematical Journal
Pub Date : 2024-04-29 DOI: 10.1007/s11253-024-02298-8
Xiaoying Han, Peter E. Kloeden

A Dong–Hopfield neural lattice model with random external forcing and delayed response to the evolution of interconnection weights is developed and studied. The interconnection weights evolve according to the Hebbian learning rule with a decay term and contribute to changes in the states after a short delay. The lattice system is first reformulated as a coupled functional-ordinary differential equation system on an appropriate product space. Then it is shown that the solution of the system exists and is unique. Furthermore, it is demonstrated that the system of equations generates a continuous random dynamical system. Finally, the existence of random attractors for the random dynamical system generated by the Dong–Hopfield model is established.

本文建立并研究了一个具有随机外部强迫和延迟响应互联权重演化的 Dong-Hopfield 神经晶格模型。互联权重根据带有衰减项的海比学习规则演化，并在短暂延迟后对状态变化做出贡献。首先将晶格系统重新表述为适当乘积空间上的耦合函数-常微分方程系统。然后证明该系统的解是存在的，并且是唯一的。此外，还证明了方程系统生成了一个连续的随机动力系统。最后，证明了由 Dong-Hopfield 模型生成的随机动力系统存在随机吸引子。
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引用次数: 0
Ideal Turbulence as a Kind of Disturbed Chaos: Brief Essay 作为一种受扰混沌的理想湍流：简论
IF 0.5 4区 数学 Q4 Mathematics
Ukrainian Mathematical Journal
Pub Date : 2024-04-29 DOI: 10.1007/s11253-024-02297-9
Olena Romanenko, Abdyvali Akbergenov

We outline key points of the concept of ideal turbulence offering novel scenarios for distributed chaos based not on the geometric-dynamical complexity of the attractor but on the extremely complex spatial structure of elements of the attractor. Ideal turbulence is observed in idealized (without internal resistance) models of various processes related to electromagnetic or acoustic oscillations. This idealization significantly simplifies the analysis and, at the same time, in many cases, provides a quite adequate description of real processes.

我们概述了理想湍流概念的要点，它不是基于吸引子的几何-动力学复杂性，而是基于吸引子元素极其复杂的空间结构，为分布式混沌提供了新的方案。在与电磁或声学振荡有关的各种过程的理想化（无内阻）模型中，可以观察到理想湍流。这种理想化大大简化了分析，同时，在许多情况下，对实际过程提供了相当充分的描述。
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引用次数: 0
A Stochastic Interpretation of the Parametrix Method 参数矩阵法的随机解释
IF 0.5 4区 数学 Q4 Mathematics
Ukrainian Mathematical Journal
Pub Date : 2024-04-23 DOI: 10.1007/s11253-024-02287-x
A. Kohatsu-Higa

We revisit, in a didactic manner and by using stochastic analysis, the parametrix method and its application to unbiased simulation. We consider, in particular, the case of one-dimensional diffusions without drift.

我们以说教的方式，通过随机分析，重温了参数矩阵法及其在无偏模拟中的应用。我们特别考虑了无漂移的一维扩散情况。
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引用次数: 0
On Reflected Diffusions in Cones and Cylinders 论锥体和圆柱体中的反射扩散
IF 0.5 4区 数学 Q4 Mathematics
Ukrainian Mathematical Journal
Pub Date : 2024-04-22 DOI: 10.1007/s11253-024-02288-w
Oleksii Kulyk, Andrey Pilipenko, Sylvie Roelly

Let X be a diffusion in a cone with oblique reflection at the boundary. We study the question whether X reaches the vertex of the cone for a finite time with positive probability. We propose a new probabilistic method of investigation connected with the long-term behavior of the diffusion reflected in a cylinder.

假设 X 是锥体中的扩散，边界处有斜反射。我们研究的问题是 X 是否在有限时间内以正概率到达圆锥的顶点。我们提出了一种新的概率研究方法，它与圆柱体中反射扩散的长期行为有关。
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引用次数: 0
Strong Measurable Continuous Modifications of Stochastic Flows 随机流的强可测量连续修正
IF 0.5 4区 数学 Q4 Mathematics
Ukrainian Mathematical Journal
Pub Date : 2024-04-22 DOI: 10.1007/s11253-024-02289-9
Olivier Raimond, Georgii Riabov
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引用次数: 0
Feynman–Kac Representation for Parabolic Anderson Equations with General Gaussian Noise 具有一般高斯噪声的抛物线安德森方程的费曼-卡克表示法
IF 0.5 4区 数学 Q4 Mathematics
Ukrainian Mathematical Journal
Pub Date : 2024-04-22 DOI: 10.1007/s11253-024-02290-2
Xia Chen
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引用次数: 0
On the Asymptotics of Solutions of Stochastic Differential Equations with Jumps 论有跳跃的随机微分方程解的渐近性
IF 0.5 4区 数学 Q4 Mathematics
Ukrainian Mathematical Journal
Pub Date : 2024-04-22 DOI: 10.1007/s11253-024-02291-1
Viktor Yuskovych
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引用次数: 0
Diffusion in Media with Membranes and Some Nonlocal Parabolic Problems 有膜介质中的扩散和一些非局部抛物问题
IF 0.5 4区 数学 Q4 Mathematics
Ukrainian Mathematical Journal
Pub Date : 2024-04-20 DOI: 10.1007/s11253-024-02285-z
Bohdan Kopytko, Mykhailo Osypchuk, Roman Shevchuk

We establish the classical solvability of a certain conjugation problem for one-dimensional (with respect to a spatial variable) Kolmogorov backward equation with discontinuous coefficients and some versions of the general nonlocal Feller–Wentzell boundary condition given on nonsmooth boundaries of the considered curvilinear domains. In addition, we prove, that the two-parameter Feller semigroup defined by the solution of this problem describes some inhomogeneous diffusion process with moving membranes on the given region of the real line. We also show the relationship between the constructed process and the generalized diffusion in a sense of M. I. Portenko.

我们建立了一维（关于空间变量）科尔莫哥罗夫反向方程的某个共轭问题的经典可解性，该方程具有不连续系数和在所考虑的曲线域的非光滑边界上给出的某些版本的一般非局部费勒-文采尔边界条件。此外，我们还证明，由该问题的解定义的双参数费勒半群描述了实线给定区域内具有移动膜的某些非均质扩散过程。我们还展示了所构建的过程与 M. I. Portenko 意义上的广义扩散之间的关系。
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引用次数: 0
Mykola Ivanovych Portenko (On His 80th Birthday) 米科拉-伊万诺维奇-波尔滕科（80 岁生日）
IF 0.5 4区 数学 Q4 Mathematics
Ukrainian Mathematical Journal
Pub Date : 2024-04-20 DOI: 10.1007/s11253-024-02284-0
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引用次数: 0
Andriy Anatoliyovych Dorogovtsev (On His 60th Birthday) 安德烈-阿纳托利耶维奇-多罗戈夫采夫（在他 60 岁生日之际）
IF 0.5 4区 数学 Q4 Mathematics
Ukrainian Mathematical Journal
Pub Date : 2024-04-20 DOI: 10.1007/s11253-024-02283-1
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引用次数: 0
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