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1.
Stability analysis of a virus infection model with humoral immunity response and two time delays
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Hui Miao Zhidong Teng Chengjun Kang Ahmadjan Muhammadhaji 《Mathematical Methods in the Applied Sciences》2016,39(12):3434-3449
In this paper, we investigate the dynamical properties for a model of delay differential equations, which describes a virus‐immune interaction in vivo. By analyzing corresponding characteristic equations, the local stability of the equilibria for infection‐free, antibody‐free, and antibody response and the existence of Hopf bifurcation with antibody response delay as a bifurcation parameter at the antibody‐activated infection equilibrium are established, respectively. Global stability of the equilibria for infection‐free, antibody‐free, and antibody response, respectively, also are established by applying the Lyapunov functionals method. The numerical simulations are performed in order to illustrate the dynamical behavior of the model. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
2.
Jinhu Xu Yicang Zhou Yiqun Li Yali Yang 《Mathematical Methods in the Applied Sciences》2016,39(18):5427-5435
A virus infection model with time delays and humoral immunity has been investigated. Mathematical analysis shows that the global dynamics of the model is fully determined by the basic reproduction numbers of the virus and the immune response, R0 and R1. The infection‐free equilibrium P0 is globally asymptotically stable when R0≤1. The infection equilibrium without immunity P1 is globally asymptotically stable when R1≤1 < R0. The infection equilibrium with immunity P2 is globally asymptotically stable when R1>1. The expression of the basic reproduction number of the immune response R1 implies that the immune response reduces the concentration of free virus as R1>1. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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Hopf bifurcation analysis of a density predator-prey model with crowley-martin functional response and two time delays
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In this paper, a delayed density dependent predator-prey model with Crowley-Martin functional response and two time delays for the predator is considered. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the system is addressed and the existence of Hopf bifurcation at the coexistence equilibrium is established. With the help of normal form method and center manifold theorem, some explicit formulas determining the direction of Hopf bifurcation and the stability of bifurcating period solutions are derived. Finally, numerical simulations are given to illustrate the theoretical results. 相似文献
5.
I. S. Kashchenko 《Doklady Mathematics》2016,94(2):578-582
The behavior of solutions near an equilibrium of differential equations with two large different-order delays is studied. In critical cases, special equations (namely, quasi-normal forms) determining the dynamics of the original problem are constructed. As a rule, they have the form of nonlinear parabolic equations with two spatial variables. Asymptotic formulas are derived showing the relation between the solutions of a quasi-normal form and the original equation. The case of a small coefficient multiplying the term with a larger delay is studied separately. 相似文献
6.
Alexander M. Gouskov Sergey A. Voronov Henri Paris Stephen A. Batzer 《Communications in Nonlinear Science & Numerical Simulation》2002,7(4)
The dynamics of turning by a tool head with two rows, each containing several cutters, is considered. A mathematical model of a process with two interdependent delays with the possibility of cutting discontinuity is analyzed. The domains of dynamic instability are derived, and the influence of technological parameters on system response is presented. The numeric analysis show that there exists specific conditions for given regimes in which one row of cutters produces an intermittent chip form while the other row produces continuous chips. It is demonstrated that the contribution of parametric excitation by shape roughness of an imperfect (unmachined) cylindrical workpiece surface is not substantial due to the special filtering properties of cutters that are uniformly distributed circumferentially along the tool head. 相似文献
7.
Yukihiko Nakata 《Journal of Mathematical Analysis and Applications》2011,375(1):14-27
In this paper, we investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in vivo. The model has two distributed time delays describing time needed for infection of cell and virus replication. Our model admits three possible equilibria, an uninfected equilibrium and infected equilibrium with or without immune response depending on the basic reproduction number for viral infection R0 and for CTL response R1 such that R1<R0. It is shown that there always exists one equilibrium which is globally asymptotically stable by employing the method of Lyapunov functional. More specifically, the uninfected equilibrium is globally asymptotically stable if R0?1, an infected equilibrium without immune response is globally asymptotically stable if R1?1<R0 and an infected equilibrium with immune response is globally asymptotically stable if R1>1. The immune activation has a positive role in the reduction of the infection cells and the increasing of the uninfected cells if R1>1. 相似文献
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构建了具有两个时滞的广义Logistic模型,分情况讨论了系统正平衡点发生局部Hopf分支和稳定性切换的条件,分析了分支点关于系统参数的单调性和极限性质.数值模拟佐证了理论结果,展示了周期振动,倍周期分支,混沌等复杂的动力学行为. 相似文献
10.
A 6-dimension dynamical schistosomiasis model incorporating five time delays is established in this paper. Two equilibrium points: a disease free equilibrium and an endemic equilibrium, are calculated respectively. The stability behaviors at the disease free equilibrium are analysed. Both analytical and numerical results are presented that prepatent periods in infection can affect the schistosomiasis transmission significantly. Thus, two effective measures on schistosomiasis prevention and control are obtained: lengthening the prepatent period in susceptible snails, and prolonging the incubation periods in miracidia and cercaria by temperature control or drug restraint. And then, numerical simulations are given to illustrate the validity and effectiveness of the model. At last a discussion is provided about our results and further work. 相似文献
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In this paper, we analyze a augmented IS-LM business cycle model with the capital accumulation equation that two time delays are considered in investment processes according to Kalecki’s idea. Applying stability switch criteria and Hopf bifurcation theory, we prove that time delays cause the equilibrium to lose or gain stability and Hopf bifurcation occurs. 相似文献
12.
Effects of time delays on bifurcation and chaos in a non-autonomous system with multiple time delays
《Chaos, solitons, and fractals》2007,31(1):39-53
Time delays are often sources of complex behavior in dynamic systems. Yet its complexity needs to be further explored, particularly when multiple time delays are present. As a purpose to gain insight into such complexity under multiple time delays, we investigate the mechanism for the action of multiple time delays on a particular non-autonomous system in this paper. The original mathematical model under consideration is a Duffing oscillator with harmonic excitation. A delayed system is obtained by adding delayed feedbacks to the original system. Two time delays are involved in such system, one of which in the displacement feedback and the other in the velocity feedback. The time delays are taken as adjustable parameters to study their effects on the dynamics of the system. Firstly, the stability of the trivial equilibrium of the linearized system is discussed and the condition under which the equilibrium loses its stability is obtained. This leads to a critical stability boundary where Hopf bifurcation or double Hopf bifurcation may occur. Then, the chaotic behavior of such system is investigated in detail. Particular emphasis is laid on the effect of delay difference between two time delays on the chaotic properties. A Melnikov’s analysis is employed to obtain the necessary condition for onset of chaos resulting from homoclinic bifurcation. And numerical analyses via the bifurcation diagram and the top Lyapunov exponent are carried out to show the actual time delay effect. Both the results obtained by the two analyses show that the delay difference between two time delays plays a very important role in inducing or suppressing chaos, so that it can be taken as a simple but efficient “switch” to control the motion of a system: either from order to chaos or from chaos to order. 相似文献
13.
Hopf bifurcation in a predator-prey system with Holling type III functional response and time delays
Zizhen Zhang Huizhong Yang Ming Fu 《Journal of Applied Mathematics and Computing》2014,44(1-2):337-356
This paper is concerned with a delayed predator-prey system with modified Leslie-Gower and Holling type III schemes. By analyzing the associated characteristic equation, its local stability and the existence of periodic solutions via Hopf bifurcation with respect to both delays are obtained. Based on the normal form method and center manifold theorem, the formulaes for determining the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are derived. Finally, some numerical simulations to illustrate the theoretical analysis are also carried out. 相似文献
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In this paper, we study a new SVEIRS infectious disease model with pulse and two time delays. The pulse vaccination strategy is used as an effective strategy for the elimination of infectious disease. The model consists of a set of integro-differential equations. The existence and global attractivity of ‘infection-free’ periodic solution, permanence of an endemic model are investigated. 相似文献
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In this paper, a free boundary problem modeling tumor growth with two discrete delays is studied. The delays respectively represents the time taken for cells to undergo mitosis and the time taken for the cell to modify the rate of cell loss due to apoptosis. We show the influence of time delays on the Hopf bifurcation when one of delays as a bifurcation parameter. 相似文献
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《Mathematical Methods in the Applied Sciences》2018,41(13):4943-4954
In this paper, we study finite‐time stability of an oscillating system with 2 delays. To derive a bounded of state vector, we use a representation of explicit solution involving 2‐delayed matrix polynomial of 2 indices after deriving some fundamental estimates for such delayed matrix polynomial of 2 indices. A sufficient condition is given. Finally, an example is given to demonstrate the application of the main result. 相似文献
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In this paper, the dynamical behavior of a virus dynamics model with CTL immune response is studied. Sufficient conditions for the asymptotical stability of a disease-free equilibrium, an immune-free equilibrium and an endemic equilibrium are obtained. We prove that there exists a threshold value of the infection rate b beyond which the endemic equilibrium bifurcates from the immune-free one. Still for increasing b values, the endemic equilibrium bifurcates towards a periodic solution. We further analyze the orbital stability of the periodic orbits arising from bifurcation by applying Poore’s condition. Numerical simulation with some hypothetical sets of data has been done to support the analytical findings. 相似文献
18.
《Nonlinear Analysis: Real World Applications》2008,9(3):725-746
We consider systems of delay differential equations representing the models containing three cells with any time-delayed connections. Global stability, delay-independent and delay-dependent local stability are studied, the existence of local and global periodic solutions is investigated. We give the stability conditions, respectively, and show that the local periodic solutions can be extended globally after certain critical values of delay. 相似文献
19.
《Nonlinear Analysis: Real World Applications》2008,9(2):547-561
Many of the existing predator–prey models on stage structured populations are some ordinary differential equations (ODE) or models without a disturbing effect of human behavior. In reality, death of the juvenile during its immature stage and catching or poisoning for the prey or predator occur continuously. From this basic standpoint, we formulate a general and robust prey-dependent consumption predator–prey model with periodic harvesting (catching or poisoning) for the prey and stage structure for the predator with constant maturation time delay (through-stage time delay) and perform a systematic mathematical and ecological study. We show that the conditions for global attractivity of the ‘predator-extinction’ (‘predator-eradication’) periodic solution and permanence of the population of the model depend on time delay, so, we call it “profitless”. We also show that constant maturation time delay and impulsive catching or poisoning for the prey can bring great effects on the dynamics of system by numerical analysis. In this paper, the main feature is that we introduce time delay and pulse into the predator–prey (natural enemy–pest) model with age structure, exhibit a new modeling method which is applied to investigate impulsive delay differential equations, and give some reasonable suggestions for pest management. 相似文献
20.
C. E. de Avellar S. A. S. Marconato 《Bulletin of the Brazilian Mathematical Society》1990,21(1):51-58
For linear difference equations with coefficients and delays varying in time, sufficient conditions are given, in the scalar case, the zero solution to be stable. 相似文献