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Threshold Dynamics of a Degenerate Diffusive HBV Infection Model with DNA-Containing Capsids in Heterogeneous Environment 在异质环境中含 DNA 头壳的退化扩散型 HBV 感染模型的阈值动态变化
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-03-14 DOI: 10.1007/s00332-024-10017-7
Yu Yang, Cheng-Hsiung Hsu, Lan Zou, Jinling Zhou
{"title":"Threshold Dynamics of a Degenerate Diffusive HBV Infection Model with DNA-Containing Capsids in Heterogeneous Environment","authors":"Yu Yang, Cheng-Hsiung Hsu, Lan Zou, Jinling Zhou","doi":"10.1007/s00332-024-10017-7","DOIUrl":"https://doi.org/10.1007/s00332-024-10017-7","url":null,"abstract":"<p>This paper is concerned with threshold dynamics of a degenerate diffusive HBV infection model with DNA-containing capsids in heterogeneous environment. We firstly address the existence of global solutions, uniform and ultimate boundedness of solutions, asymptotic smoothness of semiflows and existence of a connected global attractor for the diffusive model. Then, we identify the basic reproduction number <span>({mathcal {R}}_0)</span> and establish a threshold-type result for the disease eradication or uniform persistence when <span>({mathcal {R}}_0le 1)</span> or <span>({mathcal {R}}_0&gt;1)</span>, respectively. Especially, when <span>({mathcal {R}}_0&gt;1)</span> and the diffusion rate of capsids or the diffusion rate of virions is zero, we further show that the model admits a unique infection steady state which is globally attractive. Our results indicate that the pathogen can be eliminated by limiting the mobility of the capsids or virions.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"69 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Curvature Driven Complexity in the Defocusing Parametric Nonlinear Schrödinger System 离焦参数非线性薛定谔系统中曲率驱动的复杂性
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-02-28 DOI: 10.1007/s00332-024-10016-8
Keith Promislow, Abba Ramadan
{"title":"Curvature Driven Complexity in the Defocusing Parametric Nonlinear Schrödinger System","authors":"Keith Promislow, Abba Ramadan","doi":"10.1007/s00332-024-10016-8","DOIUrl":"https://doi.org/10.1007/s00332-024-10016-8","url":null,"abstract":"<p>The parametric nonlinear Schrödinger equation models a variety of parametrically forced and damped dispersive waves. For the defocusing regime, we derive a normal velocity for the evolution of curved dark-soliton fronts that represent a <span>(pi )</span>-phase shift across a thin interface. We establish a simple mechanism through which the parametric term transitions the normal velocity evolution from a curvature-driven flow to motion against curvature regularized by surface diffusion of curvature. In the former case interfacial length shrinks, while in the latter case interface length generically grows until self-intersection followed by a transition to complex motion.\u0000</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"17 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140003268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Effective Estimation of Trapping/Stability Regions and Bilateral Solutions’ Bounds for Some Multidimensional Nonlinear Systems with Time-Varying Coefficients 某些时变系数多维非线性系统的陷阱/稳定区域和双边解边界的有效估计
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-02-28 DOI: 10.1007/s00332-024-10013-x
{"title":"Effective Estimation of Trapping/Stability Regions and Bilateral Solutions’ Bounds for Some Multidimensional Nonlinear Systems with Time-Varying Coefficients","authors":"","doi":"10.1007/s00332-024-10013-x","DOIUrl":"https://doi.org/10.1007/s00332-024-10013-x","url":null,"abstract":"<h3>Abstract</h3> <p>Assessment of the stability/boundedness of solutions to nonlinear systems with variable coefficients brings long-standing and challenging problems which emerge in various application domains. These problems naturally evolved into more arduous and largely open problems concerned with the estimation of the corresponding stability/boundedness regions. This paper develops a novel approach furnishing computationally tractable boundedness/stability criteria which underscores a methodology providing recursive estimation of the boundaries of the trapping/stability regions for a broad class of multidimensional and nonlinear systems with variable nonperiodic coefficients. Furthermore, our approach naturally conveys the bilateral bounds for the norms of solutions to the corresponding systems via the application of successive approximations which are introduced in this paper. The developed techniques are validated in inclusive simulations which endorse their applications to systems with large and complex nonlinear components and bounded in-norm time-varying disturbances.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"135 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140003162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Super-Exponential Convergence Rate of a Nonlinear Continuous Data Assimilation Algorithm: The 2D Navier–Stokes Equation Paradigm 非线性连续数据同化算法的超指数收敛率：二维纳维-斯托克斯方程范例
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-02-24 DOI: 10.1007/s00332-024-10014-w
Elizabeth Carlson, Adam Larios, Edriss S. Titi
{"title":"Super-Exponential Convergence Rate of a Nonlinear Continuous Data Assimilation Algorithm: The 2D Navier–Stokes Equation Paradigm","authors":"Elizabeth Carlson, Adam Larios, Edriss S. Titi","doi":"10.1007/s00332-024-10014-w","DOIUrl":"https://doi.org/10.1007/s00332-024-10014-w","url":null,"abstract":"<p>We study a nonlinear-nudging modification of the Azouani–Olson–Titi continuous data assimilation (downscaling) algorithm for the 2D incompressible Navier–Stokes equations. We give a rigorous proof that the nonlinear-nudging system is globally well posed and, moreover, that its solutions converge to the true solution exponentially fast in time. Furthermore, we also prove that once the error has decreased below a certain order one threshold, the convergence becomes double exponentially fast in time, up until a precision determined by the sparsity of the observed data. In addition, we demonstrate the applicability of the analytical and sharpness of the results computationally.\u0000</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"5 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139950441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 Two-Component Sasa–Satsuma Equation: Large-Time Asymptotics on the Line 双分量萨萨摩方程：线性大时间渐近线
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-02-24 DOI: 10.1007/s00332-024-10015-9
{"title":"A Two-Component Sasa–Satsuma Equation: Large-Time Asymptotics on the Line","authors":"","doi":"10.1007/s00332-024-10015-9","DOIUrl":"https://doi.org/10.1007/s00332-024-10015-9","url":null,"abstract":"<h3>Abstract</h3> <p>We consider the initial value problem for a two-component Sasa–Satsuma equation associated with a <span> <span>(4times 4)</span> </span> Lax pair with decaying initial data on the line. By utilizing the spectral analysis, the solution of the two-component Sasa–Satsuma system is transformed into the solution of a <span> <span>(4times 4)</span> </span> matrix Riemann–Hilbert problem. Then, the long-time asymptotics of the solution is obtained by means of the nonlinear steepest descent method of Deift and Zhou for oscillatory Riemann–Hilbert problems. We show that there are three main regions in the half-plane <span> <span>(-infty&lt;x&lt;infty )</span> </span>, <span> <span>(t&gt;0)</span> </span>, where the asymptotics has qualitatively different forms: a left fast decaying sector, a central Painlevé sector where the asymptotics is described in terms of the solution to a system of coupled Painlevé II equations, which is related to a <span> <span>(4times 4)</span> </span> matrix Riemann–Hilbert problem, and a right slowly decaying oscillatory sector. </p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"3 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139950440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
An Optimal Control Approach to the Problem of the Longest Self-Supporting Structure 最长自支撑结构问题的最优控制方法
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-02-21 DOI: 10.1007/s00332-023-10011-5
Giacomo Vecchiato, Michele Palladino, Pierangelo Marcati
{"title":"An Optimal Control Approach to the Problem of the Longest Self-Supporting Structure","authors":"Giacomo Vecchiato, Michele Palladino, Pierangelo Marcati","doi":"10.1007/s00332-023-10011-5","DOIUrl":"https://doi.org/10.1007/s00332-023-10011-5","url":null,"abstract":"<p>The characterization of the self-supporting slender structure with the furthest length is of interest both from a mechanical and biological point of view. Indeed, from a mechanical perspective, this classical problem was developed and studied with different methods, for example using similarity solutions and stable manifolds. However, none of them led to a complete analytical solution. On the other hand, plant structures such as tree branches or searcher shoots in climbing plants can be considered elastic cantilevered beams. In this paper, we formulate the problem as a non-convex optimisation problem with mixed state constraints. The problem is solved by analysing the corresponding relaxation. With this method, it is possible to obtain an analytical characterization of the cross-section</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"14 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139927575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Cortical Divisive Normalization from Wilson–Cowan Neural Dynamics 从威尔逊-考文神经动力学看皮层分裂归一化问题
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-02-15 DOI: 10.1007/s00332-023-10009-z
Jesús Malo, José Juan Esteve-Taboada, Marcelo Bertalmío
{"title":"Cortical Divisive Normalization from Wilson–Cowan Neural Dynamics","authors":"Jesús Malo, José Juan Esteve-Taboada, Marcelo Bertalmío","doi":"10.1007/s00332-023-10009-z","DOIUrl":"https://doi.org/10.1007/s00332-023-10009-z","url":null,"abstract":"<p>Divisive Normalization and the Wilson–Cowan equations are well-known influential models of nonlinear neural interaction (Carandini and Heeger in Nat Rev Neurosci 13(1):51, 2012; Wilson and Cowan in Kybernetik 13(2):55, 1973). However, they have been always treated as different approaches and have not been analytically related yet. In this work, we show that Divisive Normalization can be derived from the Wilson–Cowan dynamics. Specifically, assuming that Divisive Normalization is the steady state of the Wilson–Cowan differential equations, we find that the kernel that controls neural interactions in Divisive Normalization depends on the Wilson–Cowan kernel but also depends on the signal. A standard stability analysis of a Wilson–Cowan model with the parameters obtained from our relation shows that the Divisive Normalization solution is a stable node. This stability suggests the appropriateness of our steady state assumption. The proposed theory provides a mechanistic foundation for the suggestions that have been done on the need of signal-dependent Divisive Normalization in Coen-Cagli et al. (PLoS Comput Biol 8(3):e1002405, 2012). Moreover, this theory explains the modifications that had to be introduced ad hoc in Gaussian kernels of Divisive Normalization in Martinez-Garcia et al. (Front Neurosci 13:8, 2019) to reproduce contrast responses in V1 cortex. Finally, the derived relation implies that the Wilson–Cowan dynamics also reproduce visual masking and subjective image distortion, which up to now had been explained mainly via Divisive Normalization.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"3 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139770628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Martingale Solutions in Stochastic Fluid–Structure Interaction 随机流固相互作用中的马丁格尔解
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-02-08 DOI: 10.1007/s00332-023-10012-4
Dominic Breit, Prince Romeo Mensah, Thamsanqa Castern Moyo
{"title":"Martingale Solutions in Stochastic Fluid–Structure Interaction","authors":"Dominic Breit, Prince Romeo Mensah, Thamsanqa Castern Moyo","doi":"10.1007/s00332-023-10012-4","DOIUrl":"https://doi.org/10.1007/s00332-023-10012-4","url":null,"abstract":"<p>We consider a viscous incompressible fluid interacting with a linearly elastic shell of Koiter type which is located at some part of the boundary. Recently models with stochastic perturbation in the shell equation have been proposed in the literature but only analysed in simplified cases. We investigate the full model with transport noise, where (a part of) the boundary of the fluid domain is randomly moving in time. We prove the existence of a weak martingale solution to the underlying system.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"16 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139770526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Applications of Nijenhuis Geometry V: Geodesic Equivalence and Finite-Dimensional Reductions of Integrable Quasilinear Systems 尼延胡斯几何的应用 V：积分准线性系统的测地等效性和有限维还原
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-01-29 DOI: 10.1007/s00332-023-10008-0
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
{"title":"Applications of Nijenhuis Geometry V: Geodesic Equivalence and Finite-Dimensional Reductions of Integrable Quasilinear Systems","authors":"Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev","doi":"10.1007/s00332-023-10008-0","DOIUrl":"https://doi.org/10.1007/s00332-023-10008-0","url":null,"abstract":"<p>We describe all metrics geodesically compatible with a <span>(textrm{gl})</span>-regular Nijenhuis operator <i>L</i>. The set of such metrics is large enough so that a generic local curve <span>(gamma )</span> is a geodesic for a suitable metric <i>g</i> from this set. Next, we show that a certain evolutionary PDE system of hydrodynamic type constructed from <i>L</i> preserves the property of <span>(gamma )</span> to be a <i>g</i>-geodesic. This implies that every metric <i>g</i> geodesically compatible with <i>L</i> gives us a finite-dimensional reduction of this PDE system. We show that its restriction onto the set of <i>g</i>-geodesics is naturally equivalent to the Poisson action of <span>(mathbb {R}^n)</span> on the cotangent bundle generated by the integrals coming from geodesic compatibility.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"86 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139583262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 a Chemotactic Host–Pathogen Model: Boundedness, Aggregation, and Segregation 关于趋化性宿主-病原体模型：边界、聚集和隔离
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-01-29 DOI: 10.1007/s00332-023-10010-6
Guodong Liu, Hao Wang, Xiaoyan Zhang
{"title":"On a Chemotactic Host–Pathogen Model: Boundedness, Aggregation, and Segregation","authors":"Guodong Liu, Hao Wang, Xiaoyan Zhang","doi":"10.1007/s00332-023-10010-6","DOIUrl":"https://doi.org/10.1007/s00332-023-10010-6","url":null,"abstract":"<p>This study formulates a host–pathogen model driven by cross-diffusion to examine the effect of chemotaxis on solution dynamics and spatial structures. The negative binomial incidence mechanism is incorporated to illustrate the transmission process by pathogens. In terms of the magnitude of chemotaxis, the global solvability of the model is extensively studied by employing semigroup methods, loop arguments, and energy estimates. In a limiting case, the necessary conditions for chemotaxis-driven instability are established regarding the degree of chemotactic attraction. Spatial aggregation may occur along strong chemotaxis in a two-dimensional domain due to solution explosion. We further observe that spatial segregation appears for short-lived free pathogens in a one-dimensional domain, whereas strong chemotactic repulsion homogenizes the infected hosts and thus fails to segregate host groups effectively.\u0000</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"153 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139583410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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