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ON THE STABILITY OF PERIODIC SOLUTIONS OF PIECEWISE SMOOTH PERIODIC DIFFERENTIAL EQUATIONS
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作者 Maoan HAN Yan YE 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1524-1535,共12页
In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic sol... In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic solution.We also present examples of some applications. 展开更多
关键词 periodic solution Poincarémap periodic equation stability
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TIME PERIODIC SOLUTIONS TO THE EVOLUTIONARY OSEEN MODEL FOR A GENERALIZED NEWTONIAN INCOMPRESSIBLE FLUID
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作者 岑金夏 Stanislaw MIGóRSKI +1 位作者 Emilio VILCHES 曾生达 《Acta Mathematica Scientia》 SCIE CSCD 2023年第4期1645-1667,共23页
In this paper we study a nonstationary Oseen model for a generalized Newtonian incompressible fluid with a time periodic condition and a multivalued,nonmonotone friction law.First,a variational formulation of the mode... In this paper we study a nonstationary Oseen model for a generalized Newtonian incompressible fluid with a time periodic condition and a multivalued,nonmonotone friction law.First,a variational formulation of the model is obtained;that is a nonlinear boundary hemivariational inequality of parabolic type for the velocity field.Then,an abstract first-order evolutionary hemivariational inequality in the framework of an evolution triple of spaces is investigated.Under mild assumptions,the nonemptiness and weak compactness of the set of periodic solutions to the abstract inequality are proven.Furthermore,a uniqueness theorem for the abstract inequality is established by using a monotonicity argument.Finally,we employ the theoretical results to examine the nonstationary Oseen model. 展开更多
关键词 nonstationary Oseen model Newtonian incompressible fluid hemivariational inequality periodic solution generalized subgradient
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Permanence and periodic solutions of delayed predator-prey system with impulse 被引量:1
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作者 SHI Hong-bo 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2010年第3期264-276,共13页
The existence of positive periodic solution of a generalized semi-ratio-dependent predator-prey system with time delay and impulse is studied by using the continuation theorem based on the coincidence degree theory. T... The existence of positive periodic solution of a generalized semi-ratio-dependent predator-prey system with time delay and impulse is studied by using the continuation theorem based on the coincidence degree theory. The permanence of the system is also considered. The results partially improve and extend some known criteria. 展开更多
关键词 predator-prey system IMPULSE periodic solution PERMANENCE coincidence degree.
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Existence of Four Periodic Solutions of a Ratio-Dependent Predator-Prey Model with Exploited Terms 被引量:1
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作者 TIAN Desheng ZHANG Zhengqiu 《Wuhan University Journal of Natural Sciences》 CAS 2008年第1期1-5,共5页
We study a non-autonomous ratio-dependent predator-prey model with exploited terms. This model is of periodic coefficients, which incorporates the periodicity of the varying environment. By means of the coincidence de... We study a non-autonomous ratio-dependent predator-prey model with exploited terms. This model is of periodic coefficients, which incorporates the periodicity of the varying environment. By means of the coincidence degree theory, we establish sufficient conditions for the existence of at least four positive periodic solutions of this model. 展开更多
关键词 predator-prey model RATIO-DEPENDENT exploited term periodic solution coincidence degree
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A note on periodic solutions for semi-ratio-dependent predator-prey systems 被引量:1
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作者 LIU Xiu-xiang School of Mathematical Sciences, South China Normal University, Guangdong 510631, China 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2010年第1期1-8,共8页
This note investigates the existence of periodic solutions for semi-ratio-dependent predator-prey models with functional response. New sharp criteria without any other nontrivial assumptions are presented by the invar... This note investigates the existence of periodic solutions for semi-ratio-dependent predator-prey models with functional response. New sharp criteria without any other nontrivial assumptions are presented by the invariance property of homotopy and analysis technique, which improve and extend many previous work. Some interesting numerical examples are given to illustrate our results. 展开更多
关键词 periodic solutions predator-prey system functional response.
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Periodic Solutions of Periodic Delay Predator-Prey System with Nonmonotonic Functional Response 被引量:1
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作者 宋永利 韩茂安 《Journal of Shanghai Jiaotong university(Science)》 EI 2003年第1期107-110,共4页
By using the continuation theorem of coincidence degree theory, sufficient conditions are obtained for the existence of positive periodic solutions of a delayed predator prey system with nonmonotonic functional respon... By using the continuation theorem of coincidence degree theory, sufficient conditions are obtained for the existence of positive periodic solutions of a delayed predator prey system with nonmonotonic functional response in a periodic environment. 展开更多
关键词 predator prey system periodic solution coincidence degree
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PERIODIC SOLUTIONS FOR GENERALIZED PREDATOR-PREY SYSTEMS WITH TIME DELAY AND DIFFUSION
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作者 李必文 《Acta Mathematica Scientia》 SCIE CSCD 2004年第1期151-160,共10页
A set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for delayed generalized predator-prey dispersion systemwhere ai(t),bi(t) and Di(t)(i = 1, 2) axe positive c... A set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for delayed generalized predator-prey dispersion systemwhere ai(t),bi(t) and Di(t)(i = 1, 2) axe positive continuous T-periodic functions, gi(t,xi) (i = 1,2) and h(t,y) are continuous and T-periodic with respect to t and h(t,y) > 0 for y>0,t, y∈R,pi(x)(i=1,2) are continuous and monotonously increasing functions, and Pi(xi)>0 for xi>0. 展开更多
关键词 Positive periodic solution continuation theorem of coincidence degree predator-prey system DIFFUSION DELAY
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Existence of Positive Periodic Solutions for the Predator-Prey Difference System with Beddington-DeAngelis Functional Response and Time Delays
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作者 王烈 陈斯养 《Journal of Southwest Jiaotong University(English Edition)》 2010年第3期260-270,共11页
A nonautonomous predator-prey difference model with Beddington-DeAngelis functional response, diffusion, and time delays is investigated. The model consists of n competing preys and one predator, and the predator and ... A nonautonomous predator-prey difference model with Beddington-DeAngelis functional response, diffusion, and time delays is investigated. The model consists of n competing preys and one predator, and the predator and one prey are confined to one patch. First, eon^pts and results concerning the continuation theorem of coincidence degree are summarized. Then, a system of algebraic equations is proved to have a unique solution. Finally, the sufficient conditions for the existence of a difference system are established. The result is substantiated through numerical simulation. 展开更多
关键词 predator-prey system Positive periodic solution Difference equation
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Positive Periodic Solutions of Nonautonomous Delayed Predator-Prey System with Pulse Controls
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作者 Bin Wang Shunqiang Shi Ping Luo 《Journal of Applied Mathematics and Physics》 2021年第7期1452-1467,共16页
In this paper, a biological model for two predators and one prey with impulses and periodic delays is considered. By assuming that one predator consumes prey according to Holling II functional response while the other... In this paper, a biological model for two predators and one prey with impulses and periodic delays is considered. By assuming that one predator consumes prey according to Holling II functional response while the other predators consume prey according to the Beddington-DeAngelis functional response, based on the coincidence degree theory, the existence of positive periodic solutions of nonautonomous predator-prey system with impulses and periodic delays is obtained under suitable conditions. 展开更多
关键词 Positive periodic solution predator-prey IMPULSES Delays Continuation Theorem
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Existence of Periodic Solutions for Higher Order Autonomous Birkhoff Systems 被引量:3
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作者 陈向炜 梅凤翔 《Journal of Beijing Institute of Technology》 EI CAS 2000年第2期125-130,共6页
Qualitative methods of ordinary differential equation and Liapunov center theorem were used to study the existence of periodic solutions for higher order autonomous Birkhoff systems. For higher order autonomous Birkho... Qualitative methods of ordinary differential equation and Liapunov center theorem were used to study the existence of periodic solutions for higher order autonomous Birkhoff systems. For higher order autonomous Birkhoff systems, the character of the characteristic roots of the Fréchet derivative C was obtained. Furthermore the existence theorem of periodic solutions was obtained by using Liapunov center theorem, and an example was presented to illustrate the results. 展开更多
关键词 Birkhoff system Liapunov center theorem periodic solution
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On the Existence of Periodic Solutions of a Class Nonlinear Differential Systems 被引量:1
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作者 李林 徐琛梅 《Chinese Quarterly Journal of Mathematics》 CSCD 2002年第4期69-77,共9页
One method to show the existence of ω-periodic system is given. This method is based on the ultimately boundedness of the solution of the systems. By using comparing theorem and discussing some one dimensional equati... One method to show the existence of ω-periodic system is given. This method is based on the ultimately boundedness of the solution of the systems. By using comparing theorem and discussing some one dimensional equations the main results are obtained. 展开更多
关键词 differential system periodic solutions BOUNDEDNESS
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ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR NONLINEAR SYSTEM WITH MULTIPLE DELAYS 被引量:6
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作者 曹显兵 《应用数学和力学》 CSCD 北大核心 2003年第1期105-110,共6页
The existence of T_periodic solutions of the nonlinear system with multiple delays is studied. By using the topological degree method, sufficient conditions are obtained for the existence of T_periodic solutions. As a... The existence of T_periodic solutions of the nonlinear system with multiple delays is studied. By using the topological degree method, sufficient conditions are obtained for the existence of T_periodic solutions. As an application, the existence of positive periodic solution for a logarithmic population model is established under some conditions. 展开更多
关键词 多滞量 周期解 拓扑度 周期扰动非线性系统 单种群对数模型
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Exponential stability and existence of periodic solutions for a class of recurrent neural networks with delays 被引量:1
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作者 戴志娟 《Journal of Southeast University(English Edition)》 EI CAS 2006年第2期286-293,共8页
Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays (RNNs) are studied. By employing the inequality α∏k=1^m ... Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays (RNNs) are studied. By employing the inequality α∏k=1^m bk^qk≤1/r ∑qkbk^r+1/rα^r(α≥0,bk≥0,qk〉0,with ∑k=1^m qk=r-1,r≥1, constructing suitable Lyapunov r k=l k=l functions and applying the homeomorphism theory, a family of simple and new sufficient conditions are given ensuring the global exponential stability and the existence of periodic solutions of RNNs. The results extend and improve the results of earlier publications. 展开更多
关键词 recurrent neural network global exponential stability periodic solution delay HOMEOMORPHISM Lyapunov function
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Bifurcations, Analytical and Non-Analytical Traveling Wave Solutions of (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation
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作者 Dahe Feng Jibin Li Airen Zhou 《Applied Mathematics》 2024年第8期543-567,共25页
For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits ... For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation. 展开更多
关键词 (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation BIFURCATIONS Phase Portrait Analytical periodic Wave solution periodic Cusp Wave solution
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PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS
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作者 Zhenhai LIU Nikolaos S.PAPAGEORGIOU 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1280-1300,共21页
We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the con... We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems. 展开更多
关键词 periodic boundary condition time-dependent maximal monotone operator convex and nonconvex problems extremal solutions strong relaxation
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Existence of Periodic Solutions for Generalized Liénard-Typed Functional Differential Equations
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作者 贺小明 葛渭高 单文锐 《Journal of Beijing Institute of Technology》 EI CAS 2002年第3期325-328,共4页
The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are ... The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are established for the existence of periodic solutions and some previous results are extended. 展开更多
关键词 functional differential equation periodic solution coincidence degree
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Existence of Periodic Solutions of Nonlinear Neutral Differential Equation with Deviating Argument
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作者 任景莉 葛渭高 《Journal of Beijing Institute of Technology》 EI CAS 2002年第4期439-443,共5页
Existence criteria is established for the periodic solution of the nonlinear neutral delay differential equation x′(t)=f(t,x(t),x(t-τ 1(t)),x′(t-τ 2(t)))+p(t) by means of an abstract continuous theorem of k-set ... Existence criteria is established for the periodic solution of the nonlinear neutral delay differential equation x′(t)=f(t,x(t),x(t-τ 1(t)),x′(t-τ 2(t)))+p(t) by means of an abstract continuous theorem of k-set contractive operator and some analysis technique. 展开更多
关键词 neutral delay differential equation periodic solution Fredholm operator k-set contractive operator
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Dynamics and Exact Solutions of (1 + 1)-Dimensional Generalized Boussinesq Equation with Time-Space Dispersion Term
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作者 Dahe Feng Jibin Li Jianjun Jiao 《Journal of Applied Mathematics and Physics》 2024年第8期2723-2737,共15页
We study exact solutions to (1 + 1)-dimensional generalized Boussinesq equation with time-space dispersion term by making use of improved sub-equation method, and analyse the dynamical behavior and exact solutions of ... We study exact solutions to (1 + 1)-dimensional generalized Boussinesq equation with time-space dispersion term by making use of improved sub-equation method, and analyse the dynamical behavior and exact solutions of the sub-equation after constructing the nonlinear transformation and constraint conditions. Accordingly, we obtain twenty families of exact solutions such as analytical and singular solitons and singular periodic waves. In addition, we discuss the impact of system parameters on wave propagation. 展开更多
关键词 Generalized Boussinesq Equation Improved Sub-Equation Method BIFURCATION Soliton solution periodic solution
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Existence of Many and Infinitely Many Periodic Solutions for Some Types of Differential Delay Equations
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作者 葛渭高 《Journal of Beijing Institute of Technology》 EI CAS 1993年第1期5-14,共10页
J.Kaplan and J.Yorke's method is extended to establish the exis- tence of many and infinitely many periodic solutions for the DDEs (t) =±f(x(t-1))±f(x(t-2))and (t)=±f(x(t-1).
关键词 difference differential equation periodic solution SYMMETRY
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Diversity of Rogue Wave Solutions to the (1+1)-Dimensional Boussinesq Equation
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作者 Xiaoming Wang Jingjie Huang 《Journal of Applied Mathematics and Physics》 2024年第2期458-467,共10页
A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics ... A periodically homoclinic solution and some rogue wave solutions of (1+1)-dimensional Boussinesq equation are obtained via the limit behavior of parameters and different polynomial functions. Besides, the mathematics reasons for different spatiotemporal structures of rogue waves are analyzed using the extreme value theory of the two-variables function. The diversity of spatiotemporal structures not only depends on the disturbance parameter u0 </sub>but also has a relationship with the other parameters c<sub>0</sub>, α, β. 展开更多
关键词 Boussinesq Equation Rogue wave periodically Homoclinic solution Spatiotemporal Structure
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