A gradually splitting iterative algorithm is suggested in this article to optimizing the medicine storing cabinet design. This method, basing on the least type solution, analyses the baffle spacing type to achieve a substantial redundancy reduction rate, thus to reduce the redundancy, This is done by firstly statistically analyzing the data via Excel, and secondly providing a classified redundant curve fitting chart via matlab to establish a reasonable horizontal and vertical version of spacing type, as well as by calculating the least number of storing cabinets needed, which turns out to prove the rationality of applying this method to establish storing cabinets' specifications.

The stability and bifurcation behaviors of feedback control difference system with time delay are investigated. The sufficient conditions for the local asymptotic stability of the positive equilibrium are achieved based on the theory of characteristic value and Jury criterion. It chooses a parameter of the system as the bifurcation parameter and uses bifurca-tion theory and the center manifold theorem, it gets that the difference model undergoes a flip bifurcation at an exceptive value of the bifurcation parameter, and more it analyzes the existence conditions, normal form and direction of the bifurca-tion. Numerical examples are carried out to illustrate the correctness and realizability of theoretical results.

讨论了中立型双时滞Logistic模型的稳定性及分支存在性.应用Jury判据得到正平衡态局部渐近稳定的充分条件;运用中心流形定理和分支理论并以种群的内禀增长率为分支参数,给出了模型Flip分支和N-S分支存在性条件与分支方向,简略给出了模型F-N-S分支存在的充要条件;利用中国1981-2010年人口数据得到模型中参数的拟合数值,驻证了理论的正确性,并对未来人口控制方向提出建议.

讨论了具时滞与分段常数变量的捕食-食饵生态模型的稳定性及Neimark-Sacker分支;通过计算得到连续模型对应的差分模型,基于特征值理论和Schur-Cohn判据得到正平衡态局部渐进稳定的充分条件;以食饵的内禀增长率为分支参数,运用分支理论和中心流形定理分析了Neimark-Sacker分支的存在性与稳定性条件;通过举例和数值模拟验证了理论的正确性。

The dynamics of the feedback control model on a single population with piecewise constant arguments and interference are investigated in this paper. A difference model which can equi-valently describe the dynamical behavior of the original differential model is deduced. Based on the analysis of the eigenvalues and Schur-Cohn criterion, the su?cient conditions for local asymptotic stability of the positive equilibrium are achieved. Moreover, by choosing the intrinsic growth rate of the population as the bifurcation parameter and applying the bifurcation and center manifold theories, the existence conditions for the Neimark-Sacker bifurcation of this difference model is derived. Finally, some numerical examples substantiating our theoretical predictions are given and the numerical simulations also show that: 1) the dynamics of the single population of feedback control model are very complex when we consider piecewise constant arguments and interference; and 2) the positive equilibrium of the model switches from stable to unstable as the intrinsic growth rate of population increases beyond a critical value, at which the unique supercritical Neimark-Sacker bifurcation will occur.

The stability and bifurcation behavior of Flip bifurcation behavior of neutral type discrete Logistic system with time delay are investigated in present work.Firstly,the sufficient conditions for the local asymptotic stability of the positive equilibrium are achieved based on the theory of characteristic value and Jury criterion.Secondly,by choosing the intrinsic rate as the bifurcation parameter and using bifurcation theory and the center manifold theorem,we get that the discrete model undergoes a flip bifurcation at an exceptive value of the bifurcation parameter.Finally,numerical examples carry out to justify the main results in this work.

The stability and bifurcation behavior of a population model with piecewise con-stant arguments are investigated in this paper. The discrete model determining the dynamical behavior of corresponding differential model is achieved by calculation. Firstly, the sufficient conditions for the local asymptotic stability of the steady state are achieved in three aspects based on the linearized stability analysis. Secondly, by choosing the parameter r as the bifurcation parameter and using the bifurcation theory, we find that the discrete equation undergoes a flip bifurcation at an excep-tive value of the parameter r. Finally, numerical examples are carried out to justify the main results in this work.

本文研究一类带有分段常数变量的Lorenz系统的稳定性和分支行为.首先通过计算转化得到Lorenz系统对应的差分系统,利用线性稳定性理论讨论平衡点局部渐近稳定的充要条件.其次选择差分系统三个参数的一个参数为分支参数,利用分支理论研究平衡点处产生Neimark-Sacker分支不变闭曲线的充要条件,并使用分支理论给出判断分支不变闭曲线的稳定性的阈值.最后数值模拟验证了理论分析的正确性.

T he stability and bifurcations of a single population of ratio-dependent density re-striction model with piecewise constant arguments and time delay are investigated .The local stability sufficient conditions of the positive equilibrium are derived by using the theory of characteristic value and Jury criterion .Furthermore the range of the parameter for existence of Neimark-Sacker bifurcation and Flip bifurcation of this model and the direction ,stability of N-S bifurcation are achieved by using the bifurcation theory and the center manifold theo-rem ;finally ,some examples and numerical simulations are presented to illustrate the correct-ness and realizability of our theoretical results .

The stability of equilibrium point and bifurcation analysis of a predator-prey model with piecewise constant arguments and harvest was studied.Sufficient conditions for the local asymptotically stability of this model was derived by using the Jury criterion.Also,conditions for the existence of bifurcation was discussed by applying the center manifold theorem.At last,some numerical examples supporting our theoretical predictions were given.

A delayed stage-structured single-species model with disease in infancy and vaccination is investigated.Using limit system theorem and constructing Liapunov function,the sufficient conditions for the global asymptotically stability of the positive equilibrium point and the infection-free equilibrium point are obtained.The results show that in the certain immunization coverage rate,the disease will eventually become extinct when the birth rate of the species is located in an interval,and when the birth rate is large than a threshold,the disease will eventually become an endemic.

Constructing Lyapunov functional method,this paper gave a sufficient condition to global attractivity of the zero solution of Neutral linear equation with multiple delay.Meanwhile the examples were given to illustrate the usefulness of the theorem.

为讨论具有时滞、干扰和分段常数变量的单种群比率密度制约模型的稳定性,Neimark-Sacker分支的存在性以及稳定性.利用特征值理论和Jury判据给出模型正平衡态局部渐近稳定的充分条件及分支参数范围,基于规范化理论及中心流形定理,研究了分支的方向及稳定性；通过实例与数值模拟验证所得结论的正确性、可实现性和模型复杂的动力学行为.

A delayed prey-predator system with disease in prey and predator was investigated. First the su?cient conditions for the existence of the positive equilibrium point and the infection-free equilibrium point were acquired, and then the nonlinear characteristic equation was acquired using the method of characteristic roots. Next the su?cient conditions that the equilibrium points are local asymptotically stability were obtained. Furthermore the Hopf bifurcation behavior of the equilibrium point time was discussed. At last some numerical simulations were carried out to support the theoretical analysis of the research.

The permanence and global stability of a non-autonomous predator-prey discrete model, which is consisted by n preys and m predators, with Beddington-DeAngelis functional response and time delays are investigated. Using the comparison principle of the difference equations, the sufficient condition that the discrete system is permanent is acquired directly. The sufficient conditions which ensure the global stability of the discrete system are obtained through the valuation methods. For periodic case, the sufficient conditions are established for the existence and the global stability of positive periodic solutions by the fixed point principle.

The stability and Neimark-Sacker(N-S) bifurcation of a single population harvest model with time delay and piecewise constant variables are discussed.The range of the parameter for the local stability and the existence of N-S bifurcation of this model are derived,by using the theory of characteristic value,it is proved that the model undergoes N-S bifurcation when r=r0=b[eb-2+((eb-2)2+4)1/2]/2(eb-1).The direction and stability of N-S bifurcation are derived by using the bifurcation theory and the center manifold theorem;it is proved that the only stable(unstable) closed unchanged curve appears if d0(0).Some examples and numerical simulations are presented to illustrate the correctness and realizability of theoretical results and the complex dynamical behaviors of this model.

The Hopf bifurcation in Host-Parasitoid model with the distributed and discrete delay is investigated.With time lag as a parameter,sufficient conditions of the asymptotically stability of the model and of the existence of the hopf bifurcation by using the theory of characteristic value.some numerical examples supporting our theoretical predictions are also given.

The Hopf-bifurcation in Host-Parasitoid model with discrete and continuous delay is investigated.With time lag as the parameter,sufficient conditions for asymptotically stability of sole positive equilibrium state in the system and for the existence of Hopf bifurcation are derived by using the theory of characteristic value.Furthermore,the direction of periodic solution of bifurcation occurred at its critical value and the stability are analysed by using the normal form theory and the centre manifold theorem,the computation formulae for calculating its direction and stability are presented as well.Finally,Matlab is employed to validate the examples,the consistency of our theoretical predictions and the numerical computation are supported.

The stability and Hopf bifurcation for a kind of predator system with time delay is discussed.Appying Hurwitz discriminant method and eigenvalue theory,the sufficient condition of equilibrium being local asymptotic stability and the condition of Hopf bifurcation existence are obtained.By using Matlab software package,the fitting graph of solution curve is given.The feasibility of theorem conditions is also shown by an example.

The stability and Hopf bifurcation of a class of ecological model with discrete delays and Holling type functional response are investigated.Sufficient conditions for the linear asymptotic stability of the positive equilibrium of the system are obtained by using the theory of characteristic value.The conditions for Hopf bifurcation existence and the stability of the bifurcation periodic solution are discussed by regarding the delay as a parameter.The previous theorems and conclusions are verified by some examples.The solution curves about various parameters are achieved by Matlab.The different figures are compared and analyzed.