{"title":"Stability analysis of an age-structured SIR model with nonlocal diffusion and indirect contacts","authors":"Nikhil Chanauria, Syed Abbas","doi":"10.3934/dcdsb.2023191","DOIUrl":"https://doi.org/10.3934/dcdsb.2023191","url":null,"abstract":"","PeriodicalId":51015,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series B","volume":"80 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025800","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}
{"title":"Hopf-Hopf bifurcation in a predator-prey model with nonlocal competition and refuge in prey","authors":"Yuxin Ma, Ruizhi Yang","doi":"10.3934/dcdsb.2023193","DOIUrl":"https://doi.org/10.3934/dcdsb.2023193","url":null,"abstract":"","PeriodicalId":51015,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series B","volume":"2012 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025808","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}
{"title":"Global existence in a two-species chemotaxis system with signal-dependent sensitivity and logistic source","authors":"Axiu Shu","doi":"10.3934/dcdsb.2023102","DOIUrl":"https://doi.org/10.3934/dcdsb.2023102","url":null,"abstract":"","PeriodicalId":51015,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series B","volume":"22 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025952","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}
{"title":"Random attractors and invariant measures for stochastic convective Brinkman-Forchheimer equations on 2D and 3D unbounded domains","authors":"Kush Kinra, Manil T. Mohan","doi":"10.3934/dcdsb.2023100","DOIUrl":"https://doi.org/10.3934/dcdsb.2023100","url":null,"abstract":"","PeriodicalId":51015,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series B","volume":"106 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025793","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}
This paper is concerned with the large deviation principle of the stochastic reaction-diffusion lattice systems defined on the N-dimensional integer set, where the nonlinear drift term is locally Lipschitz continuous with polynomial growth of any degree and the nonlinear diffusion term is locally Lipschitz continuous with linear growth. We first prove the convergence of the solutions of the controlled stochastic lattice systems, and then establish the large deviations by the weak convergence method based on the equivalence of the large deviation principle and the Laplace principle.
{"title":"Large deviation principles of stochastic reaction-diffusion lattice systems","authors":"Bixiang Wang","doi":"10.3934/dcdsb.2023135","DOIUrl":"https://doi.org/10.3934/dcdsb.2023135","url":null,"abstract":"This paper is concerned with the large deviation principle of the stochastic reaction-diffusion lattice systems defined on the N-dimensional integer set, where the nonlinear drift term is locally Lipschitz continuous with polynomial growth of any degree and the nonlinear diffusion term is locally Lipschitz continuous with linear growth. We first prove the convergence of the solutions of the controlled stochastic lattice systems, and then establish the large deviations by the weak convergence method based on the equivalence of the large deviation principle and the Laplace principle.","PeriodicalId":51015,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series B","volume":"8 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83878756","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}
This paper is devoted to a study of infinite horizon optimal control problems with time discounting and time averaging criteria in discrete time. It is known that these problems are related to certain infinite-dimensional linear programming problems, but compactness of the state constraint is a common assumption imposed in analysis of these LP problems. In this paper, we consider an unbounded state constraint and use Alexandroff compactification to carry out the analysis. We also establish asymptotic relationships between the optimal values of problems with time discounting and long-run average criteria.
{"title":"Compactification method in linear programming approach to infinite-horizon optimal control problems with a noncompact state constraint","authors":"I. Shvartsman","doi":"10.3934/dcdsb.2023087","DOIUrl":"https://doi.org/10.3934/dcdsb.2023087","url":null,"abstract":"This paper is devoted to a study of infinite horizon optimal control problems with time discounting and time averaging criteria in discrete time. It is known that these problems are related to certain infinite-dimensional linear programming problems, but compactness of the state constraint is a common assumption imposed in analysis of these LP problems. In this paper, we consider an unbounded state constraint and use Alexandroff compactification to carry out the analysis. We also establish asymptotic relationships between the optimal values of problems with time discounting and long-run average criteria.","PeriodicalId":51015,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series B","volume":"42 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90691859","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}
The focus of this paper is on solutions to a two-dimensional Keller-Segel system containing sub-logistic sources. We show that the presence of sub-logistic terms is adequate to prevent blow-up phenomena even in strongly degenerate Keller-Segel systems. Our proof relies on several techniques, including parabolic regularity theory in Orlicz spaces, variational arguments, interpolation inequalities, and the Moser iteration method.
{"title":"Blow-up prevention by sub-logistic sources in Keller-Segel cross diffusion type system","authors":"M. Le","doi":"10.3934/dcdsb.2023114","DOIUrl":"https://doi.org/10.3934/dcdsb.2023114","url":null,"abstract":"The focus of this paper is on solutions to a two-dimensional Keller-Segel system containing sub-logistic sources. We show that the presence of sub-logistic terms is adequate to prevent blow-up phenomena even in strongly degenerate Keller-Segel systems. Our proof relies on several techniques, including parabolic regularity theory in Orlicz spaces, variational arguments, interpolation inequalities, and the Moser iteration method.","PeriodicalId":51015,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series B","volume":"19 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87930475","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}
We consider a Keller-Segel model with non-linear porous medium type diffusion and nonlocal attractive power law interaction, focusing on potentials that are less singular than Newtonian interaction. Here, the nonlinear diffusion is chosen to be $m=frac{2d}{d+2s}$ in such a way that the associated free energy is conformal invariant and there is a family of stationary solutions $U(x)=cleft(frac{lambda}{lambda^2+|x-x_0|^2}right)^{frac{d+2s}{2}}$ for any constant $c$ and some $lambda>0, x_0 in R^d.$ We analyze under which conditions on the initial data the regime that attractive forces are stronger than diffusion occurs and classify the global existence and finite time blow-up of dynamical solutions by virtue of stationary solutions. Precisely, solutions exist globally in time if the $L^m$ norm of the initial data $|u_0|_{L^m(R^d)}$ is less than the $L^m$ norm of stationary solutions $|U(x)|_{L^m(R^d)}$. Whereas there are blowing-up solutions for $|u_0|_{L^m(R^d)}>|U(x)|_{L^m(R^d)}$.
我们考虑具有非线性多孔介质型扩散和非局部吸引幂律相互作用的Keller-Segel模型，重点关注比牛顿相互作用更少奇异的势。这里，选择非线性扩散为$m=frac{2d}{d+2s}$，使得相关的自由能是共形不变的，并且对于任意常数$c$和某些$lambda>0, x_0 in R^d.$都有稳态解族$U(x)=cleft(frac{lambda}{lambda^2+|x-x_0|^2}right)^{frac{d+2s}{2}}$。我们分析了在初始数据上出现引力强于扩散的状态的条件，并利用稳态解对动力学解的整体存在性和有限时间爆破进行了分类。准确地说，当初始数据$|u_0|_{L^m(R^d)}$的$L^m$范数小于平稳解$|U(x)|_{L^m(R^d)}$的$L^m$范数时，解在时间上全局存在。而对于$|u_0|_{L^m(R^d)}>|U(x)|_{L^m(R^d)}$，也有爆炸性的解决方案。
{"title":"The aggregation-diffusion equation with energy critical exponent","authors":"S. Bian","doi":"10.3934/dcdsb.2023126","DOIUrl":"https://doi.org/10.3934/dcdsb.2023126","url":null,"abstract":"We consider a Keller-Segel model with non-linear porous medium type diffusion and nonlocal attractive power law interaction, focusing on potentials that are less singular than Newtonian interaction. Here, the nonlinear diffusion is chosen to be $m=frac{2d}{d+2s}$ in such a way that the associated free energy is conformal invariant and there is a family of stationary solutions $U(x)=cleft(frac{lambda}{lambda^2+|x-x_0|^2}right)^{frac{d+2s}{2}}$ for any constant $c$ and some $lambda>0, x_0 in R^d.$ We analyze under which conditions on the initial data the regime that attractive forces are stronger than diffusion occurs and classify the global existence and finite time blow-up of dynamical solutions by virtue of stationary solutions. Precisely, solutions exist globally in time if the $L^m$ norm of the initial data $|u_0|_{L^m(R^d)}$ is less than the $L^m$ norm of stationary solutions $|U(x)|_{L^m(R^d)}$. Whereas there are blowing-up solutions for $|u_0|_{L^m(R^d)}>|U(x)|_{L^m(R^d)}$.","PeriodicalId":51015,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series B","volume":"24 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86522724","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}
The permutation binary neural networks are characterized by global permutation connections and local binary connections. Although the parameter space is not large, the networks exhibit various binary periodic orbits. Since analysis of all the periodic orbits is not easy, we focus on globally stable binary periodic orbits such that almost all initial points fall into the orbits. For efficient analysis, we define the standard permutation connection that represents multiple equivalent permutation connections. Applying the brute force attack to 7-dimensional networks, we present the main result: a list of standard permutation connections for all the globally stable periodic orbits. These results will be developed into detailed analysis of the networks and its engineering applications.
{"title":"A variety of globally stable periodic orbits in permutation binary neural networks","authors":"Mikito Onuki, Kento Saka, Toshimichi Saito","doi":"10.3934/dcdsb.2023078","DOIUrl":"https://doi.org/10.3934/dcdsb.2023078","url":null,"abstract":"The permutation binary neural networks are characterized by global permutation connections and local binary connections. Although the parameter space is not large, the networks exhibit various binary periodic orbits. Since analysis of all the periodic orbits is not easy, we focus on globally stable binary periodic orbits such that almost all initial points fall into the orbits. For efficient analysis, we define the standard permutation connection that represents multiple equivalent permutation connections. Applying the brute force attack to 7-dimensional networks, we present the main result: a list of standard permutation connections for all the globally stable periodic orbits. These results will be developed into detailed analysis of the networks and its engineering applications.","PeriodicalId":51015,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series B","volume":"13 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85030814","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}
In this paper, we consider a birth-death process with generator $ mathcal{L} $ and reversible invariant probability measure $ pi. $ We identify explicitly the Lipschitzian norm of the solution of the Poisson equation $ -mathcal{L} G = g-pi(g) $ for $ |g|levarphi $. This leads to some transportation-information inequalities, concentration inequalities and Cheeger-type isoperimetric inequalities. Several examples are provided to illustrate the results.
{"title":"Lipschitzian norms and functional inequalities for birth-death processes","authors":"Wei Liu","doi":"10.3934/dcdsb.2023177","DOIUrl":"https://doi.org/10.3934/dcdsb.2023177","url":null,"abstract":"In this paper, we consider a birth-death process with generator $ mathcal{L} $ and reversible invariant probability measure $ pi. $ We identify explicitly the Lipschitzian norm of the solution of the Poisson equation $ -mathcal{L} G = g-pi(g) $ for $ |g|levarphi $. This leads to some transportation-information inequalities, concentration inequalities and Cheeger-type isoperimetric inequalities. Several examples are provided to illustrate the results.","PeriodicalId":51015,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series B","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135157752","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：