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941.
杨青 《高等学校计算数学学报》2002,24(3):193-198
1 引 言考虑平面区域Ω R2上的二维问题,其数学模型为[1]-△ψ=α(p-e+N(x)),(x,t)∈Ω×J,J(0,T],(1.1) 相似文献
942.
该文探讨了单支方法关于一类中立型延迟微分方程(NDDEs)系统的整体稳定性和渐近稳定性.在适当的条件下,获得了单支方法关于NDDEs系统的一些新的非线性稳定性判据. 相似文献
943.
得到了具有多重时滞非线性差分方程x(n 1)-x(n) ∑i=1^k pi(n)fi(x(gi(n)))=0,n=0,1,2,…的每个解趋于零的充分条件。 相似文献
944.
连续型随机序列与幂函数分布的比较及几何平均的若干强极限定理 总被引:1,自引:0,他引:1
本文引入似然比概念作为一般连续型随机变量相对于乘积幂函数分布的偏差的一种随机性度量 ,运用鞅理论及分析方法 [3 - 4 ] ,得到了一种新形式的强大数定理 ,即关于随机变量几何平均 Gn(ω)=∏ni=1Xi1 /n的强极限定理 . 相似文献
945.
Recent manipulations on vertebrates showed that the fear of preda-
tors, caused by prey after they perceived predation risk, could reduce the prey''s
reproduction greatly. And it''s known that predator-prey systems with fear ef-
fect exhibit very rich dynamics. On the other hand, incorporating the time
delay into predator-prey models could also induce instability and oscillations
via Hopf bifurcation. In this paper, we are interested in studying the com-
bined effects of the fear effect and time delay on the dynamics of the classic
Lotka-Volterra predator-prey model. It''s shown that the time delay can cause
the stable equilibrium to become unstable, while the fear effect has a stabi-
lizing effect on the equilibrium. In particular, the model loses stability when
the delay varies and then regains its stability when the fear effect is stronger.
At last, by using the normal form theory and center manifold argument, we
derive explicit formulas which determine the stability and direction of periodic
solutions bifurcating from Hopf bifurcation. Numerical simulations are carried
to explain the mathematical conclusions. 相似文献
946.
In order to investigate the impact of awareness programs and time delays on the cholera outbreaks, we propose a cholera epidemic model, incorporating awareness programs by media as a separate class and two time‐delay factors. The bifurcation theory is applied to explore the variety of dynamics of this model for various combinations of the delays when R0>1. Moreover, we analyze the direction, stability, and period of the bifurcating periodic solutions arising through Hopf bifurcation by using the normal form concept and the center manifold theory. Finally, we present numerical simulations to verify the main theoretical results. 相似文献
947.
In this paper, we concentrate on the spatiotemporal patterns of a delayed reaction‐diffusion Holling‐Tanner model with Neumann boundary conditions. In particular, the time delay that is incorporated in the negative feedback of the predator density is considered as one of the principal factors to affect the dynamic behavior. Firstly, a global Turing bifurcation theorem for τ = 0 and a local Turing bifurcation theorem for τ > 0 are given. Then, further considering the degenerated situation, we derive the existence of Bogdanov‐Takens bifurcation and Turing‐Hopf bifurcation. The normal form method is used to study the explicit dynamics near the Turing‐Hopf singularity. It is shown that a pair of stable nonconstant steady states (stripe patterns) and a pair of stable spatially inhomogeneous periodic solutions (spot patterns) could be bifurcated from a positive equilibrium. Moreover, the Turing‐Turing‐Hopf–type spatiotemporal patterns, that is, a subharmonic phenomenon with two spatial wave numbers and one temporal frequency, are also found and explained theoretically. Our results imply that the interaction of Turing and Hopf instabilities can be considered as the simplest mechanism for the appearance of complex spatiotemporal dynamics. 相似文献
948.
Maxim A. Medvedev T. E. Simos Ch. Tsitouras 《Mathematical Methods in the Applied Sciences》2019,42(6):2025-2032
A four‐step method of seventh algebraic order is presented. It is tuned for addressing the special second order initial value problem. The new method is hybrid, explicit, and uses three stages per step. In addition is phase fitted. In consequence it uses variable coefficients that depend on the magnitude of the step‐size. We also present numerical tests on a set of standard problems that illustrate the efficiency of the derived method over older ones given in the relevant literature. 相似文献
949.
Jianglin Zhao Yong Yan Lizhuang Huang Run Yang 《Mathematical Methods in the Applied Sciences》2019,42(11):3831-3847
This paper deals with a diffusive toxin producing phytoplankton‐zooplankton model with maturation delay. By analyzing eigenvalues of the characteristic equation associated with delay parameter, the stability of the positive equilibrium and the existence of Hopf bifurcation are studied. Explicit results are derived for the properties of bifurcating periodic solutions by means of the normal form theory and the center manifold reduction for partial functional differential equations. Numerical simulations not only agree with the theoretical analysis but also exhibit the complex behaviors such as the period‐3, 5, 6, 7, 8, 11, and 12 solutions, cascade of period‐doubling bifurcation in period‐2, 4, quasi‐periodic solutions, and chaos. The key observation is that time delay may control harmful algae blooms (HABs). Moreover, numerical simulations show that the chaotic states induced by the period‐doubling bifurcation are purely temporal, which is stationary in space and oscillatory in time. The investigations may provide some new insights on harmful phytoplankton blooms. 相似文献
950.
Boumedine Chentouf Aissa Guesmia 《Mathematical Methods in the Applied Sciences》2019,42(13):4584-4605
This paper is concerned with the asymptotic behavior analysis of solutions to a multidimensional wave equation. Assuming that there is no displacement term in the system and taking into consideration the presence of distributed or discrete time delay, we show that the solutions exponentially converge to their stationary state. The proof mainly consists in utilizing the resolvent method. The approach adopted in this work is also used to other physical systems. 相似文献