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Qualitative Theory of Dynamical Systems最新文献

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Morse Predecomposition of an Invariant Set. 不变集的莫尔斯预分解。
IF 1.9 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2025-01-01 Epub Date: 2024-11-15 DOI: 10.1007/s12346-024-01144-3
Michał Lipiński, Konstantin Mischaikow, Marian Mrozek
{"title":"Morse Predecomposition of an Invariant Set.","authors":"Michał Lipiński, Konstantin Mischaikow, Marian Mrozek","doi":"10.1007/s12346-024-01144-3","DOIUrl":"10.1007/s12346-024-01144-3","url":null,"abstract":"<p><p>Motivated by the study of recurrent orbits and dynamics within a Morse set of a Morse decomposition we introduce the concept of Morse predecomposition of an isolated invariant set within the setting of both combinatorial and classical dynamical systems. While Morse decomposition summarizes solely the gradient part of a dynamical system, the developed generalization extends to the recurrent component as well. In particular, a chain recurrent set, which is indecomposable in terms of Morse decomposition, can be represented more finely in the Morse predecomposition framework. This generalization is achieved by forgoing the poset structure inherent to Morse decomposition and relaxing the notion of connection between Morse sets (elements of Morse decomposition) in favor of what we term 'links'. We prove that a Morse decomposition is a special case of Morse predecomposition indexed by a poset. Additionally, we show how a Morse predecomposition may be condensed back to retrieve a Morse decomposition.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"24 1","pages":"5"},"PeriodicalIF":1.9,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11568017/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142648758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Differentiability of Semi-Flow for Impulsive Evolution Equation with State-Dependent Delay 带状态延迟的脉冲演化方程的半流可微分性
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-09-18 DOI: 10.1007/s12346-024-01134-5
Weifeng Ma, Yongxiang Li
{"title":"Differentiability of Semi-Flow for Impulsive Evolution Equation with State-Dependent Delay","authors":"Weifeng Ma, Yongxiang Li","doi":"10.1007/s12346-024-01134-5","DOIUrl":"https://doi.org/10.1007/s12346-024-01134-5","url":null,"abstract":"<p>In this paper, we study the impulsive evolution equation with state-dependent delay by the theory of operator semigroup in Banach spaces. Under conditions that both nonlinearity and impulsive functions are Lipschitz continuous, we obtain the existence and uniqueness results of mild solution. Furthermore, we prove the differentiability of a semi-flow defined by a continuously differentiable solution operator under the appropriate condition.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"26 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142259688","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
Approximate Controllability of Fractional Evolution System on Non-Dense Domain 非密集域上分数演化系统的近似可控性
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-09-18 DOI: 10.1007/s12346-024-01135-4
Vikram Singh, Renu Chaudhary, Umesh Kumar, Sandeep Kumar
{"title":"Approximate Controllability of Fractional Evolution System on Non-Dense Domain","authors":"Vikram Singh, Renu Chaudhary, Umesh Kumar, Sandeep Kumar","doi":"10.1007/s12346-024-01135-4","DOIUrl":"https://doi.org/10.1007/s12346-024-01135-4","url":null,"abstract":"<p>This article explores the existence and approximate controllability of integral solutions for Hilfer fractional evolution equations in a non-dense domain. Leveraging the well-known generalized Banach contraction theorem, we establish both the existence and uniqueness of the integral solution. Furthermore, we adopt a sequential approach to derive results related to approximate controllability, without relying on the compactness of semigroups or the uniform boundedness of nonlinear functions. To validate our findings, we present and discuss an illustrative example.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"215 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142259687","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
Approximate Controllability for Semilinear Fractional Stochastic Evolution Equations 半线性分数随机演化方程的近似可控性
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-09-13 DOI: 10.1007/s12346-024-01133-6
Yiming Jiang, Jingchuang Ren, Yawei Wei, Jie Xue
{"title":"Approximate Controllability for Semilinear Fractional Stochastic Evolution Equations","authors":"Yiming Jiang, Jingchuang Ren, Yawei Wei, Jie Xue","doi":"10.1007/s12346-024-01133-6","DOIUrl":"https://doi.org/10.1007/s12346-024-01133-6","url":null,"abstract":"<p>In this paper, we show the approximate controllability for a class of semilinear fractional stochastic systems in abstract space with the Riemann–Liouville fractional derivative. The key of the proof is the existence of the mild solution for the proposed problem. These results are based on new properties of the operator obtained by the subordination principle, compact semigroup and Schauder fixed point theorem. Here we obtain the compactness of the solution operator by using Arzelà–Ascoli theorem. As an application, we establish the approximate controllability of the stochastic Rayleigh–Stokes problem for a generalized second grade fluid.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"41 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222028","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
Bifurcation of Limit Cycles for a Kind of Piecewise Smooth Differential Systems with an Elementary Center of Focus-Focus Type 一种具有焦点-焦点型基本中心的片断平滑微分系统的极限循环分岔
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-09-11 DOI: 10.1007/s12346-024-01138-1
Zheng Si, Liqin Zhao
{"title":"Bifurcation of Limit Cycles for a Kind of Piecewise Smooth Differential Systems with an Elementary Center of Focus-Focus Type","authors":"Zheng Si, Liqin Zhao","doi":"10.1007/s12346-024-01138-1","DOIUrl":"https://doi.org/10.1007/s12346-024-01138-1","url":null,"abstract":"<p>In this paper, we study the number of limit cycles <i>H</i>(<i>n</i>) bifurcating from the piecewise smooth system formed by the quadratic reversible system (r22) for <span>(yge 0)</span> and the cubic system <span>({dot{x}} =ybigl (1+{{bar{x}}}^2+y^2bigr ))</span>, <span>({dot{y}} =-{bar{x}}bigl (1+{{bar{x}}}^2+y^2bigr ))</span> for <span>(y&lt;0)</span> under the perturbations of polynomials with degree <i>n</i>, where <span>({{bar{x}}}=x-1)</span>. By using the first-order Melnikov function, it is proved that <span>(2n+3le H(n)le 2n+ 7)</span> for <span>(nge 3)</span> and the results are sharp for <span>(n=0,1,2)</span>.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"21 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227487","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
Stability of Highly Nonlinear Stochastic Delay Systems with Hybrid Switchings 具有混合开关的高度非线性随机延迟系统的稳定性
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-09-11 DOI: 10.1007/s12346-024-01131-8
Yichi Liu, Quanxin Zhu
{"title":"Stability of Highly Nonlinear Stochastic Delay Systems with Hybrid Switchings","authors":"Yichi Liu, Quanxin Zhu","doi":"10.1007/s12346-024-01131-8","DOIUrl":"https://doi.org/10.1007/s12346-024-01131-8","url":null,"abstract":"<p>Numerous studies have investigated the stability of highly nonlinear stochastic systems (HNSSs). However, previous works have primarily focused on either deterministic or random switchings. In this paper, we examine HNSSs with delays and two switching modes. First, we introduce a hybrid switching rule and construct a stopping time in segments, dividing the switching interval of the entire system into a deterministic switching interval and a stochastic switching interval. Second, we establish the existence and boundedness of the global solution of the system by using the Lyapunov function and the average dwell time method. Additionally, we prove the asymptotic stability and exponential stability of the system without relying on the linear growth condition (LGC). Finally, we provide an illustrative example to demonstrate the validity of the obtained results.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"43 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227486","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
On the Chebyshev Property of a Class of Hyperelliptic Abelian Integrals 论一类超椭圆阿贝尔积分的切比雪夫性质
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-09-11 DOI: 10.1007/s12346-024-01136-3
Yangjian Sun, Shaoqing Wang, Jiazhong Yang
{"title":"On the Chebyshev Property of a Class of Hyperelliptic Abelian Integrals","authors":"Yangjian Sun, Shaoqing Wang, Jiazhong Yang","doi":"10.1007/s12346-024-01136-3","DOIUrl":"https://doi.org/10.1007/s12346-024-01136-3","url":null,"abstract":"<p>This paper aims to demonstrate the Chebyshev property of the linear space <span>(V={sum _{i=0}^{2}alpha _ioint _{Gamma _h}x^{2i}ytextrm{d}x:alpha _0,alpha _1,alpha _2in mathbb {R},,hin Sigma })</span> (which is equivalent to that every function of <i>V</i> has at most 2 zeros, counted with multiplicity), with three hyperelliptic Abelian integrals <span>(oint _{Gamma _h}x^{2i}ytextrm{d}x ,(i=0,1,2))</span> as generators, where <span>(Gamma _h)</span> is an oval determined by <span>(H(x,y)=frac{y^2}{2}+Psi (x)=h)</span>, and <span>(Psi (x))</span> is an even polynomial of indefinite degree with real non-Morse critical points. As an application, we can obtain the exact upper bound for the number of zeros of a class of hyperelliptic Abelian integrals related to some planar polynomial Hamiltonian systems with two cusps and a nilpotent center.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"183 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222032","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
Almost Periodic Dynamics of a Delayed Patch-Constructed Nicholson’s Blowflies System 延迟补丁构建的尼科尔森吹蝇系统的近周期动力学
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-09-05 DOI: 10.1007/s12346-024-01129-2
Qian Wang, Lihong Huang
{"title":"Almost Periodic Dynamics of a Delayed Patch-Constructed Nicholson’s Blowflies System","authors":"Qian Wang, Lihong Huang","doi":"10.1007/s12346-024-01129-2","DOIUrl":"https://doi.org/10.1007/s12346-024-01129-2","url":null,"abstract":"<p>In this paper, we consider a delayed patch-constructed Nicholson’s blowflies system in almost periodic environment. By combining the innovative inequality technique with the basic properties of almost periodic functions and the fluctuation lemma, some testable criteria are achieved to verify the global exponential stability of the addressed almost periodic system under more general conditions, which improve and complement the existing literature. In particular, the assumptions employed in the established exponential stability criteria are sharp when the addressed system degenerates into the scalar Nicholson’s blowflies equation. Moreover, a numerical example is presented to illustrate the effectiveness of the theoretical results.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"12 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227490","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
Chaotic Dynamics of Conformable Maturity-Structured Cell Population Models 可变形成熟结构细胞群模型的混沌动力学
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-09-02 DOI: 10.1007/s12346-024-01132-7
Manal Menchih, Khalid Hilal, Ahmed Kajouni, Mohammad Esmael Samei
{"title":"Chaotic Dynamics of Conformable Maturity-Structured Cell Population Models","authors":"Manal Menchih, Khalid Hilal, Ahmed Kajouni, Mohammad Esmael Samei","doi":"10.1007/s12346-024-01132-7","DOIUrl":"https://doi.org/10.1007/s12346-024-01132-7","url":null,"abstract":"<p>The primary aim of this study is to analyze the chaotic dynamics of a conformable maturity structured cell partial differential equation of order <span>(zin (0,1))</span>, which extends the classical Lasota equation. To examine the chaotic behavior of our model’s solution, we initially extend certain criteria of linear chaos to conformable calculus. This extension is crucial because the solution of our model does not generate a classical semigroup but rather a <span>(c_0)</span>-<i>z</i>-semigroup. For the velocity term of our model, <span>(B(mathfrak {w})=mu mathfrak {w})</span>, where <span>(mu in mathbb {C})</span>, and the term source <span>(g(mathfrak {w}, vartheta (textsf{r}, mathfrak {w})))</span>, we utilize spectral properties of the <i>z</i>-infinitesimal generator to demonstrate chaotic behavior in the space <span>(C(textrm{J}_0, mathbb {C}))</span>, <span>(textrm{J}_0:=[0,+infty ))</span>. Furthermore, by employing conformable admissible weight functions and setting <span>(B(mathfrak {w})=1)</span>, we establish chaos in the solution <i>z</i>-semigroup, this time within the space <span>(C_{0}(textrm{J}_0, mathbb {C}))</span>.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"7 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222031","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
Second-Order Noncanonical Delay Differential Equations with Sublinear and Superlinear Terms: New Oscillation Criteria via Canonical Transform and Arithmetic–Geometric Inequality 带亚线性和超线性项的二阶非正则延迟微分方程：通过佳能变换和算术几何不等式的新振荡标准
IF 1.4 3区 数学
Qualitative Theory of Dynamical Systems Pub Date : 2024-08-29 DOI: 10.1007/s12346-024-01130-9
Ganesh Purushothaman, Kannan Suresh, Ethiraju Thandapani, Ercan Tunç
{"title":"Second-Order Noncanonical Delay Differential Equations with Sublinear and Superlinear Terms: New Oscillation Criteria via Canonical Transform and Arithmetic–Geometric Inequality","authors":"Ganesh Purushothaman, Kannan Suresh, Ethiraju Thandapani, Ercan Tunç","doi":"10.1007/s12346-024-01130-9","DOIUrl":"https://doi.org/10.1007/s12346-024-01130-9","url":null,"abstract":"<p>In this paper, the authors present new oscillation criteria for the noncanonical second-order delay differential equation with mixed nonlinearities </p><span>$$begin{aligned} (a(t)x^{prime }(t))^{prime }+ sum _{j=1}^{n} q_{j}(t) x^{alpha _{j}}(sigma _{j}(t))=0 end{aligned}$$</span><p>using an arithmetic–geometric mean inequality. We establish our results first by transforming the studied equation into canonical form and then applying a comparison technique and integral averaging method to get new oscillation criteria. Examples are provided to illustrate the importance and novelty of their main results.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"2 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142227488","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
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