Pub Date : 2023-09-23DOI: 10.1007/s10884-023-10308-9
Jane Allwright
Abstract Reaction–diffusion equations are studied on bounded, time-periodic domains with zero Dirichlet boundary conditions. The long-time behaviour is shown to depend on the principal periodic eigenvalue of a transformed periodic-parabolic problem. We prove upper and lower bounds on this eigenvalue under a range of different assumptions on the domain, and apply them to examples. The principal eigenvalue is considered as a function of the frequency, and results are given regarding its behaviour in the small and large frequency limits. A monotonicity property with respect to frequency is also proven. A reaction–diffusion problem with a class of monostable nonlinearity is then studied on a periodic domain, and we prove convergence to either zero or a unique positive periodic solution.
{"title":"Reaction–Diffusion Problems on Time-Periodic Domains","authors":"Jane Allwright","doi":"10.1007/s10884-023-10308-9","DOIUrl":"https://doi.org/10.1007/s10884-023-10308-9","url":null,"abstract":"Abstract Reaction–diffusion equations are studied on bounded, time-periodic domains with zero Dirichlet boundary conditions. The long-time behaviour is shown to depend on the principal periodic eigenvalue of a transformed periodic-parabolic problem. We prove upper and lower bounds on this eigenvalue under a range of different assumptions on the domain, and apply them to examples. The principal eigenvalue is considered as a function of the frequency, and results are given regarding its behaviour in the small and large frequency limits. A monotonicity property with respect to frequency is also proven. A reaction–diffusion problem with a class of monostable nonlinearity is then studied on a periodic domain, and we prove convergence to either zero or a unique positive periodic solution.","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135959916","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}
Pub Date : 2023-09-23DOI: 10.1007/s10884-023-10309-8
Jesús Dueñas, Carmen Núñez, Rafael Obaya
Abstract The global bifurcation diagrams for two different one-parametric perturbations ( $$+lambda x$$ +λx and $$+lambda x^2$$ +λx2 ) of a dissipative scalar nonautonomous ordinary differential equation $$x'=f(t,x)$$ x′=f(t,x) are described assuming that 0 is a constant solution, that f is recurrent in t , and that its first derivative with respect to x is a strictly concave function. The use of the skewproduct formalism allows us to identify bifurcations with changes in the number of minimal sets and in the shape of the global attractor. In the case of perturbation $$+lambda x$$ +λx , a so-called generalized pitchfork bifurcation may arise, with the particularity of lack of an analogue in autonomous dynamics. This new bifurcation pattern is extensively investigated in this work.
摘要描述了一个耗散标量非自治常微分方程$$x'=f(t,x)$$ x ' = f (t, x)的两个不同单参数扰动($$+lambda x$$ + λ x和$$+lambda x^2$$ + λ x 2)的全局分岔图，假设0是常数解，f在t中循环，其关于x的一阶导数是严格凹函数。斜积形式的使用使我们能够识别最小集数量和全局吸引子形状变化的分岔。在摄动$$+lambda x$$ + λ x的情况下，可能会出现所谓的广义干草叉分岔，其特点是在自主动力学中缺乏类似物。本文对这种新的分岔模式进行了广泛的研究。
{"title":"Generalized Pitchfork Bifurcations in D-Concave Nonautonomous Scalar Ordinary Differential Equations","authors":"Jesús Dueñas, Carmen Núñez, Rafael Obaya","doi":"10.1007/s10884-023-10309-8","DOIUrl":"https://doi.org/10.1007/s10884-023-10309-8","url":null,"abstract":"Abstract The global bifurcation diagrams for two different one-parametric perturbations ( $$+lambda x$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>+</mml:mo> <mml:mi>λ</mml:mi> <mml:mi>x</mml:mi> </mml:mrow> </mml:math> and $$+lambda x^2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>+</mml:mo> <mml:mi>λ</mml:mi> <mml:msup> <mml:mi>x</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> ) of a dissipative scalar nonautonomous ordinary differential equation $$x'=f(t,x)$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:msup> <mml:mi>x</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mo>=</mml:mo> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>,</mml:mo> <mml:mi>x</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> are described assuming that 0 is a constant solution, that f is recurrent in t , and that its first derivative with respect to x is a strictly concave function. The use of the skewproduct formalism allows us to identify bifurcations with changes in the number of minimal sets and in the shape of the global attractor. In the case of perturbation $$+lambda x$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>+</mml:mo> <mml:mi>λ</mml:mi> <mml:mi>x</mml:mi> </mml:mrow> </mml:math> , a so-called generalized pitchfork bifurcation may arise, with the particularity of lack of an analogue in autonomous dynamics. This new bifurcation pattern is extensively investigated in this work.","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135958965","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}
Pub Date : 2023-09-15DOI: 10.1007/s10884-023-10287-x
Josiney A. Souza
{"title":"Decomposition of Linear Systems on Disconnected Lie Groups","authors":"Josiney A. Souza","doi":"10.1007/s10884-023-10287-x","DOIUrl":"https://doi.org/10.1007/s10884-023-10287-x","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"356 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135436363","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}
Pub Date : 2023-09-15DOI: 10.1007/s10884-023-10307-w
Dejun Luo
{"title":"Enhanced Dissipation for Stochastic Navier–Stokes Equations with Transport Noise","authors":"Dejun Luo","doi":"10.1007/s10884-023-10307-w","DOIUrl":"https://doi.org/10.1007/s10884-023-10307-w","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"134 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135436709","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}
Pub Date : 2023-09-15DOI: 10.1007/s10884-023-10306-x
Li Ma, Shangjiang Guo
{"title":"Global Dynamics of a Diffusive Lotka–Volterra Competition Model with Stage-Structure","authors":"Li Ma, Shangjiang Guo","doi":"10.1007/s10884-023-10306-x","DOIUrl":"https://doi.org/10.1007/s10884-023-10306-x","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135436710","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}
Pub Date : 2023-09-15DOI: 10.1007/s10884-023-10285-z
Thi Minh Thao Le, Sten Madec
{"title":"Spatiotemporal Evolution of Coinfection Dynamics: A Reaction–Diffusion Model","authors":"Thi Minh Thao Le, Sten Madec","doi":"10.1007/s10884-023-10285-z","DOIUrl":"https://doi.org/10.1007/s10884-023-10285-z","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135437530","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}
Pub Date : 2023-09-02DOI: 10.1007/s10884-023-10304-z
L. Barreira, C. Valls
{"title":"Delay-Difference Equations and Stability","authors":"L. Barreira, C. Valls","doi":"10.1007/s10884-023-10304-z","DOIUrl":"https://doi.org/10.1007/s10884-023-10304-z","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44210986","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}
Pub Date : 2023-08-29DOI: 10.1007/s10884-023-10303-0
D. Dragičević, A. L. Sasu, B. Sasu, Ana Şirianţu
{"title":"Zabczyk Type Criteria for Asymptotic Behavior of Dynamical Systems and Applications","authors":"D. Dragičević, A. L. Sasu, B. Sasu, Ana Şirianţu","doi":"10.1007/s10884-023-10303-0","DOIUrl":"https://doi.org/10.1007/s10884-023-10303-0","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44626889","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":"Dynamics of a Predator–Prey Model with Memory-Based Diffusion","authors":"Yujia Wang, Chuncheng Wang, Dejun Fan, Yuming Chen","doi":"10.1007/s10884-023-10305-y","DOIUrl":"https://doi.org/10.1007/s10884-023-10305-y","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41375980","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}
Pub Date : 2023-08-27DOI: 10.1007/s10884-023-10299-7
Mingdi Huang, Shiliang Wu, Xiao-Qiang Zhao
{"title":"Propagation Dynamics for Time–Space Periodic and Partially Degenerate Reaction–Diffusion Systems with Time Delay","authors":"Mingdi Huang, Shiliang Wu, Xiao-Qiang Zhao","doi":"10.1007/s10884-023-10299-7","DOIUrl":"https://doi.org/10.1007/s10884-023-10299-7","url":null,"abstract":"","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43165074","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}
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