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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
Ukrainian Mathematical Journal Pub Date : 2024-04-29 DOI: 10.1007/s11253-024-02298-8
Xiaoying Han, Peter E. Kloeden
{"title":"Dynamics of a Random Hopfield Neural Lattice Model with Adaptive Synapses and Delayed Hebbian Learning","authors":"Xiaoying Han, Peter E. Kloeden","doi":"10.1007/s11253-024-02298-8","DOIUrl":"https://doi.org/10.1007/s11253-024-02298-8","url":null,"abstract":"<p>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.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140809754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Ukrainian Mathematical Journal Pub Date : 2024-04-29 DOI: 10.1007/s11253-024-02297-9
Olena Romanenko, Abdyvali Akbergenov
{"title":"Ideal Turbulence as a Kind of Disturbed Chaos: Brief Essay","authors":"Olena Romanenko, Abdyvali Akbergenov","doi":"10.1007/s11253-024-02297-9","DOIUrl":"https://doi.org/10.1007/s11253-024-02297-9","url":null,"abstract":"<p>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.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140809750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Ukrainian Mathematical Journal Pub Date : 2024-04-23 DOI: 10.1007/s11253-024-02287-x
A. Kohatsu-Higa
{"title":"A Stochastic Interpretation of the Parametrix Method","authors":"A. Kohatsu-Higa","doi":"10.1007/s11253-024-02287-x","DOIUrl":"https://doi.org/10.1007/s11253-024-02287-x","url":null,"abstract":"<p>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.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Ukrainian Mathematical Journal Pub Date : 2024-04-22 DOI: 10.1007/s11253-024-02288-w
Oleksii Kulyk, Andrey Pilipenko, Sylvie Roelly
{"title":"On Reflected Diffusions in Cones and Cylinders","authors":"Oleksii Kulyk, Andrey Pilipenko, Sylvie Roelly","doi":"10.1007/s11253-024-02288-w","DOIUrl":"https://doi.org/10.1007/s11253-024-02288-w","url":null,"abstract":"<p>Let <i>X</i> be a diffusion in a cone with oblique reflection at the boundary. We study the question whether <i>X</i> 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.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140797871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Ukrainian Mathematical Journal Pub Date : 2024-04-22 DOI: 10.1007/s11253-024-02289-9
Olivier Raimond, Georgii Riabov
{"title":"Strong Measurable Continuous Modifications of Stochastic Flows","authors":"Olivier Raimond, Georgii Riabov","doi":"10.1007/s11253-024-02289-9","DOIUrl":"https://doi.org/10.1007/s11253-024-02289-9","url":null,"abstract":"","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140673983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Ukrainian Mathematical Journal Pub Date : 2024-04-22 DOI: 10.1007/s11253-024-02290-2
Xia Chen
{"title":"Feynman–Kac Representation for Parabolic Anderson Equations with General Gaussian Noise","authors":"Xia Chen","doi":"10.1007/s11253-024-02290-2","DOIUrl":"https://doi.org/10.1007/s11253-024-02290-2","url":null,"abstract":"","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140675996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Ukrainian Mathematical Journal Pub Date : 2024-04-22 DOI: 10.1007/s11253-024-02291-1
Viktor Yuskovych
{"title":"On the Asymptotics of Solutions of Stochastic Differential Equations with Jumps","authors":"Viktor Yuskovych","doi":"10.1007/s11253-024-02291-1","DOIUrl":"https://doi.org/10.1007/s11253-024-02291-1","url":null,"abstract":"","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140673679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Ukrainian Mathematical Journal Pub Date : 2024-04-20 DOI: 10.1007/s11253-024-02285-z
Bohdan Kopytko, Mykhailo Osypchuk, Roman Shevchuk
{"title":"Diffusion in Media with Membranes and Some Nonlocal Parabolic Problems","authors":"Bohdan Kopytko, Mykhailo Osypchuk, Roman Shevchuk","doi":"10.1007/s11253-024-02285-z","DOIUrl":"https://doi.org/10.1007/s11253-024-02285-z","url":null,"abstract":"<p>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.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140627087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Ukrainian Mathematical Journal Pub Date : 2024-04-20 DOI: 10.1007/s11253-024-02284-0
{"title":"Mykola Ivanovych Portenko (On His 80th Birthday)","authors":"","doi":"10.1007/s11253-024-02284-0","DOIUrl":"https://doi.org/10.1007/s11253-024-02284-0","url":null,"abstract":"","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140681856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Ukrainian Mathematical Journal Pub Date : 2024-04-20 DOI: 10.1007/s11253-024-02283-1
{"title":"Andriy Anatoliyovych Dorogovtsev (On His 60th Birthday)","authors":"","doi":"10.1007/s11253-024-02283-1","DOIUrl":"https://doi.org/10.1007/s11253-024-02283-1","url":null,"abstract":"","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140680064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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