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Modeling impulsive resource inputs in host-parasitoid interactions with time delays

International Journal of Biomathematics 2018年第5期11卷 67-92页

作者： Shouzong Liu Mingzhan Huang Xinyu Song Shuai Li Huidong Cheng College of Mathematics and Statistics Xinyang Normal University Xinyang 464000 P. R. China College of Mathematics and Systems Science Shandong University of Science and Technology Qingdao 266000 P. R. China

For the interaction of parasitoids and their insect hosts in the laboratory environment, a novel mathematical model with impulsive resource inputs, stage-structure, maturation delays and negative binomial distribution is proposed. Based on the adaptability of the insect host to the environment, we study the permanence of the system in two cases and gain conditions under which the host and parasitoid species can coexist with impulsive resource inputs. We also discuss the existence of the positive periodic solution.when the system is permanent by applying a fixed point theory. Besides, we perform numerical simulations which not only confirm but also further enhance our theoretical results. The simulations show that when total input of resource is fixed, smaller input amounts with shorter periods of impulsive delivery produce smaller oscillation amplitudes for both the host and parasitoid populations at the juvenile stage. However, both the densities of adult host and adult parasitoid are not affected by the resource management strategy. Furthermore, we also reconfirm that larger maturation delays, either the host or the parasitoid＇s delay, lead to any more individuals staying at the inmature stage of the species, while the adult populations decline dramatically at the same time. On the other hand, larger host maturation delays promote the parasitoid＇s population growth at both stages, and the impact of parasitoid maturation delay on the host population is almost the same but not as dramatic. These findings give us a deeper understanding about the host parasitoid interaction in laboratory environment.

关键词： Host parasitoid model maturation delay impulsive input permanence periodic solution.

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Intermediate filament dynamics： Disassembly regulation

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International Journal of Biomathematics 2017年第1期10卷 273-294页

作者： Chengjun Sun Julien Arino Stephanie Portet School of Management and EconomicsKunming University of Science and Technology Kunming P. R. China Department of Mechanical Engineering University of Hong Kong Pokfulam Road Hong Kong Department of Mathematics University of Manitoba Winnipeg Manitoba R3T 2N2 Canada

A mechanism of intermediate filament disassembly regulation is proposed in which disas- sembly is regulated by the amount of proteins assembled in networks. It is Mso hypothe- sized that a delay might exist between regulation and actuM disassembly. Under realistic biological conditions of assembly and disassembly, it is shown that such a delay is harm- less and does not destabilize the organization of intermediate filaments in networks. However, for high rates of disassembly, the model predicts that delay can destabilize the organization, with the intermediate filament material oscillating between organizations mainly in networks and in nonfilamentous particles.

关键词： Cytoskeleton organization intermediate filaments time delay global asymp-totic stability bifurcation periodic solution.

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BIFURCATION AND SPATIOTEMPORAL PATTERNS IN A HOMOGENEOUS DIFFUSION-COMPETITION SYSTEM WITH DELAYS

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International Journal of Biomathematics 2012年第6期5卷 19-41页

作者： JIA-FANG ZHANG WAN-TONG LI XIANG-PING YAN School of Mathematics and Information Sciences Henan University Kaifeng Henan 575001 P. R. China School of Mathematics and StatisticsLanzhou University Lanzhou Gansu 730000 P. R. China Department of MathematicsLanzhou Jiaotong University Lanzhou Gansu 730070 P. R. China

A competitive LotkaVolterra reactiondiffusion system with two delays subject to Neumann boundary conditions is considered. It is well known that the positive con stant steady state of the system is globally asymptotically stable if the interspecies competition is weaker than the intraspecies one and is unstable if the interspecies com petition dominates over the intraspecies one. If the latter holds, then we show that Hopf bifurcation can occur as the parameters （delays） in the system cross some critical val ues. In particular, we prove that these Hopf bifurcations are all spatially homogeneous if the diffusive rates are suitably large, which has the same properties as Hopf bifur cation of the corresponding delayed system without diffusion. However, if the diffusive rates are suitably small, then the system generates the spatially nonhomogeneous Hopf bifurcation. Furthermore, we derive conditions for determining the direction of spatially nonhomogeneous Hopf bifurcations and the stability of bifurcating periodic solution.. These results indicate that the diffusion plays an important role for deriving the complex spatiotemporal dynamics.

关键词： LotKa-Volterra competition system time delay spatial diffusion Hopf bifur-cation periodic solution.

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HETEROCLINIC BIFURCATIONS OF A PREY-PREDATOR FISHERY MODEL WITH IMPULSIVE HARVESTING

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International Journal of Biomathematics 2013年第5期6卷 85-99页

作者： CHUNJIN WEI LANSUN CHEN Science College Jimei UniversityXiamen Fujian 361021 P. R. China Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 P. R. China

In this paper, we consider a prey-predator fishery model with Allee effect and state- dependent impulsive harvesting. First, we investigate the existence of order-1 heteroclinic cycle. Second, choosing p as a control parameter, we obtain the sufficient conditions for the existence and uniqueness of order-1 periodic solution.of system （2.3） by using the geometry theory of semi-continuous dynamic systems. Finally, on the basis of the theory of rotated vector fields, heteroclinic bifurcation to perturbed system of system （2.3） is also studied. The methods used in this paper are novel to prove the existence of order-1 heteroclinic cycle and heteroclinic bifurcations.

关键词： Rotated vector fields successor function heteroclinic cycle heteroclinicbifurcations periodic solution.

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A SHOOTING METHOD FOR THE SWIFT-HOHENBERG EQUATION

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Applied Mathematics(A Journal of Chinese Universities) 2002年第4期17卷 391-403页

作者： TaoYoushan ZhangJizhou Dept.ofAppl.Math. DonghuaUniv.Shanghai200051.China CollegeofMath.Sci. ShanghaiNormalUniv.Shanghai200234China

Stationary even single bump periodic solution. of the Swift Hohenberg equation are analyzed. The coefficient k in the equation is found to be a critical parameter. It is proved if 0periodic solution. having the same energy as the constant solution. u=0; if 1periodic solution. having the same energy as the stable states u=±k-1. The proof of the above results is based on a shooting technique, together with a linearization method and a scaling argument.

关键词： shooting technique Swift Hohenberg equation critical point periodic solution.

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A PRIORI BOUNDS FOR periodic solution. OF A KIND OF THIRD-ORDER DELAY DIFFERENTIAL EQUATION

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Applied Mathematics(A Journal of Chinese Universities) 2005年第1期20卷 59-63页

作者： GuiZhanji GeWeigao Dept.ofMath. BeijingInstituteofTechnologyBeijing100081China.／／Dept.ofMath.HainanNormalUniv.Haikou571158China. Dept.ofMath. BeijingInstituteofTechnologyBeijing100081China.

By means of continuation theorem of the coincidence degree theory, sufficient conditions are obtained for the existence of periodic solution. of a kind of third-order neutral delay functional differential equation wit... 详细信息

关键词： neutral delay third order differential equation periodic solution.

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Existence and Global Exponential Stability of periodic solution. for General Shunting Inhibitory Cellular Neural Networks with Delays

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Journal of Mathematical Research and Exposition 2010年第6期30卷 1125-1136页

作者： De Fei ZHANG Xin Song YANG Yao LONG Ping HE Department of Mathematics Honghe UniversityYunnan 661100P.R.China

By using the Leray-Schauder fixed point theorem,differential inequality techniques and constructing suitable Lyapunov functional,several sufficient conditions are obtained for the existence and global exponential stability of periodic solution. for general shunting inhibitory cellular neural networks with *** new results are obtained and some previously known results are *** example is employed to illustrate our feasible results.

关键词： shunting inhibitory cellular neural networks global exponential stability periodic solution.

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