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On β-extinction and Stability of a Stochastic Lotka-Volterra System with Infinite Delay 论具有无限延迟的随机 Lotka-Volterra 系统的 β 消亡和稳定性
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1078-7
Shu-fen Zhao
{"title":"On β-extinction and Stability of a Stochastic Lotka-Volterra System with Infinite Delay","authors":"Shu-fen Zhao","doi":"10.1007/s10255-024-1078-7","DOIUrl":"10.1007/s10255-024-1078-7","url":null,"abstract":"<div><p>In this paper, a stochastic Lotka-Volterra system with infinite delay is considered. A new concept of extinction, namely, the almost sure <i>β</i>-extinction is proposed and sufficient conditions for the solution to be almost sure <i>β</i>-extinction are obtained. When the positive equilibrium exists and the intensities of the noises are small enough, any solution of the system is attracted by the positive equilibrium. Finally, numerical simulations are carried out to support the results.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587784","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}
引用次数: 0
Traveling Fronts for a Time-periodic Population Model with Dispersal 有散布的时周期种群模型的移动前沿
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1052-4
Hai-qin Zhao
{"title":"Traveling Fronts for a Time-periodic Population Model with Dispersal","authors":"Hai-qin Zhao","doi":"10.1007/s10255-024-1052-4","DOIUrl":"10.1007/s10255-024-1052-4","url":null,"abstract":"<div><p>In this paper, we study a class of time-periodic population model with dispersal. It is well known that the existence of the periodic traveling fronts has been established. However, the uniqueness and stability of such fronts remain unsolved. In this paper, we first prove the uniqueness of non-critical periodic traveling fronts. Then, we show that all non-critical periodic traveling fronts are exponentially asymptotically stable.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587787","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}
引用次数: 0
Temporal Second-order Scheme for a Hidden-memory Variable Order Time Fractional Diffusion Equation with an Initial Singularity 具有初始奇点的隐记变阶时间分式扩散方程的时序二阶方案
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1054-2
Rui-lian Du, Zhi-zhong Sun
{"title":"Temporal Second-order Scheme for a Hidden-memory Variable Order Time Fractional Diffusion Equation with an Initial Singularity","authors":"Rui-lian Du,&nbsp;Zhi-zhong Sun","doi":"10.1007/s10255-024-1054-2","DOIUrl":"10.1007/s10255-024-1054-2","url":null,"abstract":"<div><p>In this work, a novel time-stepping <span>(overline{L1})</span> formula is developed for a hidden-memory variable-order Caputo’s fractional derivative with an initial singularity. This formula can obtain second-order accuracy and an error estimate is analyzed strictly. As an application, a fully discrete difference scheme is established for the initial-boundary value problem of a hidden-memory variable-order time fractional diffusion model. Numerical experiments are provided to support our theoretical results.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587783","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}
引用次数: 0
Chaotic Motions of the van der Pol-Duffing Oscillator Subjected to Periodic External and Parametric Excitations with Delayed Feedbacks 范德尔波尔-杜芬振荡器在周期性外部和参数激励下的混沌运动与延迟反馈
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1038-2
Liang-qiang Zhou, Fang-qi Chen
{"title":"Chaotic Motions of the van der Pol-Duffing Oscillator Subjected to Periodic External and Parametric Excitations with Delayed Feedbacks","authors":"Liang-qiang Zhou,&nbsp;Fang-qi Chen","doi":"10.1007/s10255-024-1038-2","DOIUrl":"10.1007/s10255-024-1038-2","url":null,"abstract":"<div><p>Chaotic dynamics of the van der Pol-Duffing oscillator subjected to periodic external and parametric excitations with delayed feedbacks are investigated both analytically and numerically in this manuscript. With the Melnikov method, the critical value of chaos arising from homoclinic or heteroclinic intersections is derived analytically. The feature of the critical curves separating chaotic and non-chaotic regions on the excitation frequency and the time delay is investigated analytically in detail. The monotonicity of the critical value to the excitation frequency and time delay is obtained rigorously. It is presented that there may exist a special frequency for this system. With this frequency, chaos in the sense of Melnikov may not occur for any excitation amplitudes. There also exists a uncontrollable time delay with which chaos always occurs for this system. Numerical simulations are carried out to verify the chaos threshold obtained by the analytical method.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587785","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}
引用次数: 0
A Test of U-type for Goodness-of-fit in Regression Models Through Martingale Difference Divergence 通过马丁格尔差分对回归模型拟合优度的 U 型检验
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1132-5
Kai Xu, Yan-qin Nie, Dao-jiang He
{"title":"A Test of U-type for Goodness-of-fit in Regression Models Through Martingale Difference Divergence","authors":"Kai Xu,&nbsp;Yan-qin Nie,&nbsp;Dao-jiang He","doi":"10.1007/s10255-024-1132-5","DOIUrl":"10.1007/s10255-024-1132-5","url":null,"abstract":"<div><p>Based on the martingale difference divergence, a recently proposed metric for quantifying conditional mean dependence, we introduce a consistent test of U-type for the goodness-of-fit of linear models under conditional mean restriction. Methodologically, our test allows heteroscedastic regression models without imposing any condition on the distribution of the error, utilizes effectively important information contained in the distance of the vector of covariates, has a simple form, is easy to implement, and is free of the subjective choice of parameters. Theoretically, our mathematical analysis is of own interest since it does not take advantage of the empirical process theory and provides some insights on the asymptotic behavior of U-statistic in the framework of model diagnostics. The asymptotic null distribution of the proposed test statistic is derived and its asymptotic power behavior against fixed alternatives and local alternatives converging to the null at the parametric rate is also presented. In particular, we show that its asymptotic null distribution is very different from that obtained for the true error and their differences are interestingly related to the form expression for the estimated parameter vector embodied in regression function and a martingale difference divergence matrix. Since the asymptotic null distribution of the test statistic depends on data generating process, we propose a wild bootstrap scheme to approximate its null distribution. The consistency of the bootstrap scheme is justified. Numerical studies are undertaken to show the good performance of the new test.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587786","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}
引用次数: 0
Global Dynamics of a Kawasaki Disease Vascular Endothelial Cell Injury Model with Backward Bifurcation and Hopf Bifurcation 带有后向分岔和霍普夫分岔的川崎病血管内皮细胞损伤模型的全局动力学研究
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-07-03 DOI: 10.1007/s10255-024-1096-5
Ke Guo, Wan-biao Ma
{"title":"Global Dynamics of a Kawasaki Disease Vascular Endothelial Cell Injury Model with Backward Bifurcation and Hopf Bifurcation","authors":"Ke Guo, Wan-biao Ma","doi":"10.1007/s10255-024-1096-5","DOIUrl":"https://doi.org/10.1007/s10255-024-1096-5","url":null,"abstract":"<p>Kawasaki disease (KD) is an acute, febrile, systemic vasculitis that mainly affects children under five years of age. In this paper, we propose and study a class of 5-dimensional ordinary differential equation model describing the vascular endothelial cell injury in the lesion area of KD. This model exhibits forward/backward bifurcation. It is shown that the vascular injury-free equilibrium is locally asymptotically stable if the basic reproduction number <i>R</i><sub>0</sub> &lt; 1. Further, we obtain two types of suffcient conditions for the global asymptotic stability of the vascular injury-free equilibrium, which can be applied to both the forward and backward bifurcation cases. In addition, the local and global asymptotic stability of the vascular injury equilibria and the presence of Hopf bifurcation are studied. It is also shown that the model is permanent if the basic reproduction number <i>R</i><sub>0</sub> &gt; 1, and some explicit analytic expressions of ultimate lower bounds of the solutions of the model are given. Our results suggest that the control of vascular injury in the lesion area of KD is not only correlated with the basic reproduction number <i>R</i><sub>0</sub>, but also with the growth rate of normal vascular endothelial cells promoted by the vascular endothelial growth factor.</p>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521362","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}
引用次数: 0
Equilibrium Reinsurance Strategy and Mean Residual Life Function 均衡再保险策略和平均剩余寿命函数
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1050-6
Dan-ping Li, Lv Chen, Lin-yi Qian, Wei Wang
{"title":"Equilibrium Reinsurance Strategy and Mean Residual Life Function","authors":"Dan-ping Li,&nbsp;Lv Chen,&nbsp;Lin-yi Qian,&nbsp;Wei Wang","doi":"10.1007/s10255-024-1050-6","DOIUrl":"10.1007/s10255-024-1050-6","url":null,"abstract":"<div><p>In this paper, we analyze the relationship between the equilibrium reinsurance strategy and the tail of the distribution of the risk. Since Mean Residual Life (MRL) has a close relationship with the tail of the distribution, we consider two classes of risk distributions, Decreasing Mean Residual Life (DMRL) and Increasing Mean Residual Life (IMRL) distributions, which can be used to classify light-tailed and heavy-tailed distributions, respectively. We assume that the underlying risk process is modelled by the classical Cramér-Lundberg model process. Under the mean-variance criterion, by solving the extended Hamilton-Jacobi-Bellman equation, we derive the equilibrium reinsurance strategy for the insurer and the reinsurer under DMRL and IMRL, respectively. Furthermore, we analyze how to choose the reinsurance premium to make the insurer and the reinsurer agree with the same reinsurance strategy. We find that under the case of DMRL, if the distribution and the risk aversions satisfy certain conditions, the insurer and the reinsurer can adopt a reinsurance premium to agree on a reinsurance strategy, and under the case of IMRL, the insurer and the reinsurer can only agree with each other that the insurer do not purchase the reinsurance.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256213","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}
引用次数: 0
Incidence Coloring of Outer-1-planar Graphs 外-1-平面图的入射着色
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1126-3
Meng-ke Qi, Xin Zhang
{"title":"Incidence Coloring of Outer-1-planar Graphs","authors":"Meng-ke Qi,&nbsp;Xin Zhang","doi":"10.1007/s10255-024-1126-3","DOIUrl":"10.1007/s10255-024-1126-3","url":null,"abstract":"<div><p>A graph is outer-1-planar if it can be drawn in the plane so that all vertices lie on the outer-face and each edge crosses at most one another edge. It is known that every outer-1-planar graph is a planar partial 3-tree. In this paper, we conjecture that every planar graph <i>G</i> has a proper incidence (Δ(<i>G</i>) + 2)-coloring and confirm it for outer-1-planar graphs with maximum degree at least 8 or with girth at least 4. Specifically, we prove that every outer-1-planar graph <i>G</i> has an incidence (Δ(<i>G</i>) + 3, 2)-coloring, and every outer-1-planar graph <i>G</i> with maximum degree at least 8 or with girth at least 4 has an incidence (Δ(<i>G</i>) + 2, 2)-coloring.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256357","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}
引用次数: 0
Barrier Option Pricing in Regime Switching Models with Rebates 有回扣的制度转换模型中的障碍期权定价
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1053-3
Yue-xu Zhao, Jia-yong Bao
{"title":"Barrier Option Pricing in Regime Switching Models with Rebates","authors":"Yue-xu Zhao,&nbsp;Jia-yong Bao","doi":"10.1007/s10255-024-1053-3","DOIUrl":"10.1007/s10255-024-1053-3","url":null,"abstract":"<div><p>This paper is concerned with the valuation of single and double barrier knock-out call options in a Markovian regime switching model with specific rebates. The integral formulas of the rebates are derived via matrix Wiener-Hopf factorizations and Fourier transform techniques, also, the integral representations of the option prices are constructed. Moreover, the first-passage time density functions in two-state regime model are derived. As applications, several numerical algorithms and numerical examples are presented.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256262","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}
引用次数: 0
Long-time Asymptotics for the Reverse Space-time Nonlocal Hirota Equation with Decaying Initial Value Problem: without Solitons 具有衰减初值问题的反向时空非局部广达方程的长时渐近线：无孤子
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-06-05 DOI: 10.1007/s10255-024-1121-8
Wei-qi Peng, Yong Chen
{"title":"Long-time Asymptotics for the Reverse Space-time Nonlocal Hirota Equation with Decaying Initial Value Problem: without Solitons","authors":"Wei-qi Peng,&nbsp;Yong Chen","doi":"10.1007/s10255-024-1121-8","DOIUrl":"10.1007/s10255-024-1121-8","url":null,"abstract":"<div><p>In this work, we mainly consider the Cauchy problem for the reverse space-time nonlocal Hirota equation with the initial data rapidly decaying in the solitonless sector. Start from the Lax pair, we first construct the basis Riemann-Hilbert problem for the reverse space-time nonlocal Hirota equation. Furthermore, using the approach of Deift-Zhou nonlinear steepest descent, the explicit long-time asymptotics for the reverse space-time nonlocal Hirota is derived. For the reverse space-time nonlocal Hirota equation, since the symmetries of its scattering matrix are different with the local Hirota equation, the <i>ϑ</i>(<i>λ</i><sub><i>i</i></sub>) (<i>i</i> = 0, 1) would like to be imaginary, which results in the <span>(delta _{{{rm{lambda}}_i}}^0)</span> contains an increasing <span>(t{{pm ,Imvartheta ({{rm{lambda}}_i})} over 2})</span>, and then the asymptotic behavior for nonlocal Hirota equation becomes differently.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141256245","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}
引用次数: 0
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