Nonlinear Analysis-Real World Applications最新文献_第9页

On the number of limit cycles in piecewise planar quadratic differential systems 论片面平面二次微分系统中的极限循环数

IF 2 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2024-05-04 DOI: 10.1016/j.nonrwa.2024.104124

Francisco Braun , Leonardo Pereira Costa da Cruz , Joan Torregrosa

{"title":"On the number of limit cycles in piecewise planar quadratic differential systems","authors":"Francisco Braun , Leonardo Pereira Costa da Cruz , Joan Torregrosa","doi":"10.1016/j.nonrwa.2024.104124","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104124","url":null,"abstract":"<div><p>We consider piecewise quadratic perturbations of centers of piecewise quadratic systems in two zones determined by a straight line through the origin. By means of expansions of the displacement map, we are able to find isolated zeros of it, without dealing with the unsurprising difficult integrals inherent in the usual averaging approach. We apply this technique to non-smooth perturbations of the four families of isochronous centers of the Loud family, <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span>, and <span><math><msub><mrow><mi>S</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>, as well as to non-smooth perturbations of non-smooth centers given by putting different <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>’s in each zone. To show the coverage of our approach, we apply its first order, which is equivalent to averaging theory of the first order, in perturbations of the already mentioned centers considering all the straight lines through the origin. Then we apply the second order of our approach to perturbations of the above centers for a specific oblique straight line. Here in order to argue we introduce certain blow-ups in the perturbative parameters. As a consequence of our study, we obtain examples of piecewise quadratic systems with at least 12 limit cycles. By analyzing two previous works of the literature claiming much more limit cycles we found some mistakes in the calculations. Therefore, the best lower bound for the number of limit cycles of a piecewise quadratic system is up to now the 12 limit cycles found in the present paper.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140824129","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

Optimal decay estimate and asymptotic profile for solutions to the generalized Zakharov–Kuznetsov–Burgers equation in 2D 二维广义扎哈罗夫-库兹涅佐夫-伯格斯方程解的最优衰减估计和渐近曲线

IF 2 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2024-05-03 DOI: 10.1016/j.nonrwa.2024.104130

Ikki Fukuda , Hiroyuki Hirayama

{"title":"Optimal decay estimate and asymptotic profile for solutions to the generalized Zakharov–Kuznetsov–Burgers equation in 2D","authors":"Ikki Fukuda , Hiroyuki Hirayama","doi":"10.1016/j.nonrwa.2024.104130","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104130","url":null,"abstract":"<div><p>We consider the Cauchy problem for the generalized Zakharov–Kuznetsov–Burgers equation in 2D. This is one of the nonlinear dispersive–dissipative equations, which has a spatial anisotropic dissipative term <span><math><mrow><mo>−</mo><mi>μ</mi><msub><mrow><mi>u</mi></mrow><mrow><mi>x</mi><mi>x</mi></mrow></msub></mrow></math></span>. In this paper, we prove that the solution to this problem decays at the rate of <span><math><msup><mrow><mi>t</mi></mrow><mrow><mo>−</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></msup></math></span> in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span>-sense, provided that the initial data <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow></mrow></math></span> satisfies <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> and some appropriate regularity assumptions. Moreover, we investigate the more detailed large time behavior and obtain a lower bound of the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span>-norm of the solution. As a result, we prove that the given decay rate <span><math><msup><mrow><mi>t</mi></mrow><mrow><mo>−</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></msup></math></span> of the solution to be optimal. Furthermore, combining the techniques used for the parabolic equations and for the Schr<span><math><mover><mrow><mi>o</mi></mrow><mrow><mo>̈</mo></mrow></mover></math></span>dinger equation, we derive the explicit asymptotic profile for the solution.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140825738","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

Spatio-temporal patterns and global bifurcation of a nonlinear cross-diffusion predator–prey model with prey-taxis and double Beddington–DeAngelis functional responses 具有猎物-猎物和双贝丁顿-德安吉利斯功能响应的非线性交叉扩散捕食者-猎物模型的时空模式和全局分岔

IF 2 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2024-05-03 DOI: 10.1016/j.nonrwa.2024.104133

Demou Luo , Qiru Wang

{"title":"Spatio-temporal patterns and global bifurcation of a nonlinear cross-diffusion predator–prey model with prey-taxis and double Beddington–DeAngelis functional responses","authors":"Demou Luo , Qiru Wang","doi":"10.1016/j.nonrwa.2024.104133","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104133","url":null,"abstract":"<div><p>The aim of this article is investigating the spatio-temporal patterns of a nonlinear cross-diffusion predator–prey model with prey-taxis and double Beddington–DeAngelis functional responses. First, by utilizing user-friendly version of Crandall–Rabinowitz bifurcation theory as an analytical method, the spatio-temporal patterns of positive steady state are obtained. Then, by regarding the cross-diffusion coefficient <span><math><msub><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> as a bifurcation parameter, we will derive a bifurcation theorem for the corresponding nonlinear cross-diffusion model. Moreover, by applying spectrum theory, perturbation of simple eigenvalues and linearized stability, it is discovered that the bifurcation solutions possess local stability near the bifurcating point in proper conditions. These theoretical results mean that the cross-diffusion mechanism can create a coexistence environment for the preys and predator under some circumstances. Finally, a numerical example is proposed to verify our results.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140825739","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

The role of manipulative trophically transmitted parasites in the stability of a predator–prey community 操纵性营养传播寄生虫在捕食者-猎物群落稳定性中的作用

IF 2 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2024-04-30 DOI: 10.1016/j.nonrwa.2024.104123

Jean-Christophe Poggiale , Rafael Bravo de la Parra , Ezio Venturino

{"title":"The role of manipulative trophically transmitted parasites in the stability of a predator–prey community","authors":"Jean-Christophe Poggiale , Rafael Bravo de la Parra , Ezio Venturino","doi":"10.1016/j.nonrwa.2024.104123","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104123","url":null,"abstract":"<div><p>In this paper, we are interested in the effect of a trophically transmitted parasite on the structure and dynamics of a resident predator–prey community. The parasite, apart from increasing the mortality rates of its hosts, can also change their physiology or their behaviour, which is known as trait-mediated indirect interaction. We assume that parasite transmission, which entails rapid physiological or behavioural change, is a fast process with respect to the community dynamics, including prey and predator growths and predation. This existence of different time scales allows us to provide analytical results to understand some conditions under which the parasite change the dynamics of the predator–prey community. Thus, we are able to find conditions under which indirect trait-mediated interactions induced by the parasite lead to a coexistence between predators and prey that would not occur in its absence. We also provide conditions, evolutionary deleterious, that ensure the extinction of a predator–prey community that would be viable without parasite intervention. Finally, we show situations in which the action of the parasite destabilizes the predator–prey system without eliminating it, producing oscillations, the mechanism of which is analysed.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1468121824000634/pdfft?md5=c007706a979b3aa387e052c31cc79141&pid=1-s2.0-S1468121824000634-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140816717","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

On a Stokes hemivariational inequality for incompressible fluid flows with damping 关于有阻尼的不可压缩流体流动的斯托克斯半变量不等式

IF 2 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2024-04-27 DOI: 10.1016/j.nonrwa.2024.104131

Weimin Han , Hailong Qiu , Liquan Mei

引用次数: 0

Stability and codimension 2 bifurcations in an SIR model with incubation delay 有孵化延迟的 SIR 模型的稳定性和第 2 维分岔

IF 2 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2024-04-27 DOI: 10.1016/j.nonrwa.2024.104127

Tanuja Das, Prashant K. Srivastava

{"title":"Stability and codimension 2 bifurcations in an SIR model with incubation delay","authors":"Tanuja Das, Prashant K. Srivastava","doi":"10.1016/j.nonrwa.2024.104127","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104127","url":null,"abstract":"<div><p>The aim of this paper is to investigate the complex nonlinear dynamics, such as the existence and effect of various types of bifurcations, in an infectious disease model system. An <span><math><mrow><mi>S</mi><mi>I</mi><mi>R</mi></mrow></math></span> delay model that accounts for saturated incidence, saturated treatment, and self-protection in the susceptible population is considered. The model system has a disease free equilibrium, and its local stability is determined by the basic reproduction number for any delay value. The existence of multiple endemic equilibria is obtained, and these equilibria may switch stability due to variation of bifurcation parameters. When incubation delay is zero, Bogdanov–Takens bifurcation occurs, which implies the existence of Hopf bifurcation, saddle–node, and homoclinic bifurcations. Thus, the disease will persist within or on the homoclinic loop and otherwise dies out. We also find the existence of backward bifurcation and forward (transcritical) bifurcation. The delay-induced stability switches are observed due to Hopf bifurcations, leading to endemic bubbles. Incubation delay affects the stability of equilibria when the model system has multiple endemic equilibria, so multi-stability is observed. Due to incubation delay, the two frequency Hopf–Hopf bifurcation and Bogdanov–Takens bifurcation are found. Thus, both codimension 1 and codimension 2 bifurcations in the effect of incubation delay are exhibited in this study. Numerically, we notice that with increasing incubation delay, the endemic equilibrium either changes stability (from stable to unstable or unstable to stable) or remains unstable with different frequencies of oscillations.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140807061","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

Long time asymptotics of small mass solutions for a chemotaxis-consumption system involving prescribed signal concentrations on the boundary 涉及边界上规定信号浓度的趋化-消耗系统的小质量解的长时间渐近线

IF 2 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2024-04-26 DOI: 10.1016/j.nonrwa.2024.104129

Soo-Oh Yang , Jaewook Ahn

{"title":"Long time asymptotics of small mass solutions for a chemotaxis-consumption system involving prescribed signal concentrations on the boundary","authors":"Soo-Oh Yang , Jaewook Ahn","doi":"10.1016/j.nonrwa.2024.104129","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104129","url":null,"abstract":"<div><p>This paper investigates a parabolic–elliptic chemotaxis-consumption system with signal dependent sensitivity <span><math><mrow><mi>χ</mi><mo>=</mo><mi>χ</mi><mrow><mo>(</mo><mi>c</mi><mo>)</mo></mrow></mrow></math></span> under no-flux/Dirichlet boundary conditions. For general <span><math><mi>χ</mi></math></span> which may allow singularities at <span><math><mrow><mi>c</mi><mo>=</mo><mn>0</mn></mrow></math></span>, the global existence and boundedness of radial large data solutions are established in dimensions <span><math><mrow><mi>d</mi><mo>≥</mo><mn>2</mn></mrow></math></span>. In particular, when <span><math><mrow><mi>χ</mi><mrow><mo>(</mo><mi>c</mi><mo>)</mo></mrow><mo>=</mo><mn>1</mn></mrow></math></span>, we also find that the constructed solution converges asymptotically to a nonhomogeneous steady state if the initial mass is small. On the other hand, for the system with <span><math><mrow><mi>χ</mi><mrow><mo>(</mo><mi>c</mi><mo>)</mo></mrow><mo>=</mo><mi>c</mi></mrow></math></span>, a Lyapunov-type inequality is derived. This inequality not only leads to a result on global existence of smooth solutions with non-radial large data in two dimensions but moreover, provides long-time asymptotics of non-radial <span><math><mrow><mo>(</mo><mi>d</mi><mo>=</mo><mn>2</mn><mo>)</mo></mrow></math></span> and radial <span><math><mrow><mo>(</mo><mi>d</mi><mo>≥</mo><mn>2</mn><mo>)</mo></mrow></math></span> solutions at suitably small mass levels.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140649213","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

Semilinear elliptic problems involving a fast increasing diffusion weight 涉及快速增加扩散权重的半线性椭圆问题

IF 2 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2024-04-26 DOI: 10.1016/j.nonrwa.2024.104128

Juan Arratia , Diego Ferraz , Denilson Pereira , Pedro Ubilla

引用次数: 0

Coexistence of two species with intra- and interspecific competition in an unstirred chemostat 非搅拌恒温器中两个物种的共存与种内和种间竞争

IF 2 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2024-04-21 DOI: 10.1016/j.nonrwa.2024.104125

Xuan Bai, Yao Shi, Xiongxiong Bao

引用次数: 0

The effects of diffusion and advection on the dynamics of a Lotka–Volterra competition system 扩散和平流对洛特卡伏特拉竞争系统动力学的影响

IF 2 3区数学

Nonlinear Analysis-Real World Applications Pub Date : 2024-04-21 DOI: 10.1016/j.nonrwa.2024.104126

Xiao Yan , Hua Nie

引用次数: 0