Bulletin des Sciences Mathematiques最新文献_第10页

On neutral Tannakian subcategories of loop quiver representations 论环震颤器表征的中性坦纳基亚类

IF 1.3 3区数学

Bulletin des Sciences Mathematiques Pub Date : 2024-07-31 DOI: 10.1016/j.bulsci.2024.103484

Umesh V. Dubey, Parul Keshari

引用次数: 0

Hopf bifurcation in a class of piecewise smooth near-Hamiltonian systems 一类片断平稳近哈密尔顿系统中的霍普夫分岔

IF 1.3 3区数学

Bulletin des Sciences Mathematiques Pub Date : 2024-07-24 DOI: 10.1016/j.bulsci.2024.103471

Maoan Han, Shanshan Liu

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Zero-Hopf bifurcation of limit cycles in certain differential systems 某些微分系统中极限循环的零-霍普夫分岔

IF 1.3 3区数学

Bulletin des Sciences Mathematiques Pub Date : 2024-07-24 DOI: 10.1016/j.bulsci.2024.103472

Bo Huang , Dongming Wang

{"title":"Zero-Hopf bifurcation of limit cycles in certain differential systems","authors":"Bo Huang , Dongming Wang","doi":"10.1016/j.bulsci.2024.103472","DOIUrl":"10.1016/j.bulsci.2024.103472","url":null,"abstract":"<div>This paper studies the number of limit cycles that may bifurcate from an equilibrium of an autonomous system of differential equations. The system in question is assumed to be of dimension n, have a zero-Hopf equilibrium at the origin, and consist only of homogeneous terms of order m. Denote by <math><msub><mrow><mi>H</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>)</mo></math> the maximum number of limit cycles of the system that can be detected by using the averaging method of order k. We prove that <math><msub><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>)</mo><mo>≤</mo><mo>(</mo><mi>m</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>⋅</mo><msup><mrow><mi>m</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow></msup></math> and <math><msub><mrow><mi>H</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>)</mo><mo>≤</mo><msup><mrow><mo>(</mo><mi>k</mi><mi>m</mi><mo>)</mo></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></math> for generic <math><mi>n</mi><mo>≥</mo><mn>3</mn></math>, <math><mi>m</mi><mo>≥</mo><mn>2</mn></math> and <math><mi>k</mi><mo>></mo><mn>1</mn></math>. The exact numbers of <math><msub><mrow><mi>H</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>)</mo></math> or tight bounds on the numbers are determined by computing the mixed volumes of some polynomial systems obtained from the averaged functions. Based on symbolic and algebraic computation, a general and algorithmic approach is proposed to derive sufficient conditions for a given differential system to have a prescribed number of limit cycles. The effectiveness of the proposed approach is illustrated by a family of third-order differential equations, a four-dimensional hyperchaotic differential system and a model of nuclear spin generator.</div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"195 ","pages":"Article 103472"},"PeriodicalIF":1.3,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141951437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Finite-time H∞ synchronization of semi-Markov jump neural networks with two delay components with stochastic sampled-data control 具有两个延迟分量的半马尔可夫跃迁神经网络的有限时间 H∞ 同步与随机采样数据控制

IF 1.3 3区数学

Bulletin des Sciences Mathematiques Pub Date : 2024-07-23 DOI: 10.1016/j.bulsci.2024.103482

T. Radhika, A. Chandrasekar, V. Vijayakumar

{"title":"Finite-time H∞ synchronization of semi-Markov jump neural networks with two delay components with stochastic sampled-data control","authors":"T. Radhika, A. Chandrasekar, V. Vijayakumar","doi":"10.1016/j.bulsci.2024.103482","DOIUrl":"10.1016/j.bulsci.2024.103482","url":null,"abstract":"<div>This article investigates the finite-time <math><msub><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msub></math> synchronization for semi-Markov jump neural networks with two delay components based on stochastic sampled data control. Additionally, the parametric uncertainties are randomly varying which follows the Bernoulli distributed sequences. In the stochastic sampled data control, the sampling interval <math><mo>′</mo><msup><mrow><mi>m</mi></mrow><mrow><mo>′</mo></mrow></msup></math> is supposed to be two different values in the time-varying component with given probability conditions. By constructing triple and quadruple integral term in the Lyapunov-Krasovskii functional (LKF) a new integral inequality technique is addressed to derive the main results. Dissimilar from previous literature, involving the new integral inequality, a delay dependent finite-time <math><msub><mrow><mi>H</mi></mrow><mrow><mo>∞</mo></mrow></msub></math> synchronization requirements are acquired with regard to linear matrix inequalities (LMIs). In the end, the effectiveness of the considered stochastic sampled data control finite time synchronization scheme is highlighted by numerical examples.</div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"195 ","pages":"Article 103482"},"PeriodicalIF":1.3,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141845853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Multi-index upper semicontinuity of pullback random attractors for fractional discrete FitzHugh-Nagumo systems with delays driven by Wong-Zakai approximations 王扎凯近似驱动的有延迟的分数离散菲茨休-纳古莫系统的回拉随机吸引子的多指数上半连续性

IF 1.3 3区数学

Bulletin des Sciences Mathematiques Pub Date : 2024-07-20 DOI: 10.1016/j.bulsci.2024.103483

Qiangheng Zhang

{"title":"Multi-index upper semicontinuity of pullback random attractors for fractional discrete FitzHugh-Nagumo systems with delays driven by Wong-Zakai approximations","authors":"Qiangheng Zhang","doi":"10.1016/j.bulsci.2024.103483","DOIUrl":"10.1016/j.bulsci.2024.103483","url":null,"abstract":"<div>In this paper, we consider the global well-posedness and multi-index stability of pullback random attractors for random fractional retarded lattice FitzHugh-Nagumo systems with nonlinear Wong-Zakai noise and non-autonomous forcing term. We use the idea of Caraballo et al. (2014) [2] to prove the global well-posedness. Based on the global well-posedness of the lattice FitzHugh-Nagumo system, we study the existence, uniqueness and upper semicontinuity of pullback random attractors <math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>ϱ</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>=</mo><mo>{</mo><msubsup><mrow><mi>A</mi></mrow><mrow><mi>ϱ</mi></mrow><mrow><mi>δ</mi></mrow></msubsup><mo>(</mo><mi>τ</mi><mo>,</mo><mi>ω</mi><mo>)</mo><mo>:</mo><mi>τ</mi><mo>∈</mo><mi>R</mi><mo>,</mo><mi>ω</mi><mo>∈</mo><mi>Ω</mi><mo>}</mo></math>. More precisely, we first utilize the method of tail-estimates of solution and Ascoli-Arzelà theorem to prove the existence and uniqueness of pullback random attractors, and then investigate the four types of upper semicontinuity of pullback random attractors: (1) The long time stability of pullback random attractors as the time parameter τ approaches negative infinity; (2) The upper semicontinuity of pullback random attractors as the step-length δ of the Wong-Zakai approximation tends to positive infinity; (3) The upper semicontinuity of pullback random attractors as the delay time <math><mi>ϱ</mi><mo>→</mo><mn>0</mn></math>; (4) The upper semicontinuity of pullback random attractors from non-autonomous to autonomous.</div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"195 ","pages":"Article 103483"},"PeriodicalIF":1.3,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141851578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Asymptotic behavior for kirchhoff type stochastic plate equations on unbounded domains 无界域上基尔霍夫型随机板方程的渐近行为

IF 1.3 3区数学

Bulletin des Sciences Mathematiques Pub Date : 2024-07-06 DOI: 10.1016/j.bulsci.2024.103470

Xiaobin Yao, Yang Bai

引用次数: 0

Correspondence between projective bundles over P2 and rational hypersurfaces in P4 P2 上的射影束与 <mml:math> 中的有理超曲面之间的对应关系

IF 1.3 3区数学

Bulletin des Sciences Mathematiques Pub Date : 2024-07-05 DOI: 10.1016/j.bulsci.2024.103469

Shivam Vats

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Improvement of the discrete Hardy inequality 离散哈代不等式的改进

IF 1.3 3区数学

Bulletin des Sciences Mathematiques Pub Date : 2024-07-04 DOI: 10.1016/j.bulsci.2024.103468

Prasun Roychowdhury , Durvudkhan Suragan

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Geometric estimates and comparability of Eisenman volume elements with the Bergman kernel on (C-)convex domains 艾森曼体积元素与伯格曼核在（[公式省略]-）凸域上的几何估计值和可比性

IF 1.3 3区数学

Bulletin des Sciences Mathematiques Pub Date : 2024-07-03 DOI: 10.1016/j.bulsci.2024.103467

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Commutativity of Hankel and Toeplitz operators on the Hardy space of the n-torus n 符的哈代空间上的汉克尔和托普利兹算子的交换性

IF 1.3 3区数学

Bulletin des Sciences Mathematiques Pub Date : 2024-07-01 DOI: 10.1016/j.bulsci.2024.103466

Raúl E. Curto , Gopal Datt , Bhawna Bansal Gupta

{"title":"Commutativity of Hankel and Toeplitz operators on the Hardy space of the n-torus","authors":"Raúl E. Curto , Gopal Datt , Bhawna Bansal Gupta","doi":"10.1016/j.bulsci.2024.103466","DOIUrl":"10.1016/j.bulsci.2024.103466","url":null,"abstract":"<div>We consider Hankel and Toeplitz operators on <math><msup><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msup><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math>, the Hardy space of the n-torus <math><msup><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msup></math>. Given symbols φ and ψ in <math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msup><mrow><mi>T</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math> with suitable properties, we obtain necessary and sufficient conditions for the Hankel operator <math><msub><mrow><mi>H</mi></mrow><mrow><mi>ψ</mi><mo>,</mo><mi>n</mi></mrow></msub></math> and the Toeplitz operator <math><msub><mrow><mi>T</mi></mrow><mrow><mi>φ</mi><mo>,</mo><mi>n</mi></mrow></msub></math> to commute. We then extend the study to the more general situation where no assumptions are imposed on φ, and provide new, non-trivial necessary conditions for the commutativity of <math><msub><mrow><mi>H</mi></mrow><mrow><mi>ψ</mi><mo>,</mo><mi>n</mi></mrow></msub></math> and <math><msub><mrow><mi>T</mi></mrow><mrow><mi>φ</mi><mo>,</mo><mi>n</mi></mrow></msub></math>. We also show that certain well known commutativity results between Hankel and Toeplitz operators in the one-variable case do not extend to the multivariable setting.</div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"194 ","pages":"Article 103466"},"PeriodicalIF":1.3,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141572399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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