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11.
Considerthediferenceequationwithavariabledelayxn-xn-1=F(xn,xr(n),n=n0,n0+1,…(1)where(H1):F∈C(R×R,R),F(u,v)isdecreasingwithres... 相似文献
12.
We study the expected delay in cyclic polling models with general ‘branching-type’ service disciplines. For this class of
models, which contains models with exhaustive and gated service as special cases, we obtain closed-form expressions for the
expected delay under standard heavy-traffic scalings. We identify a single parameter associated with the service discipline
at each queue, which we call the ‘exhaustiveness’. We show that the scaled expected delay figures depend on the service policies
at the queues only through the exhaustiveness of each of the service disciplines. This implies that the influence of different
service disciplines, but with the same exhaustiveness, on the expected delays at the queues becomes the same when the system
reaches saturation. This observation leads to a new classification of the service disciplines. In addition, we show monotonicity
of the scaled expected delays with respect to the exhaustiveness of the service disciplines. This induces a complete ordering
in terms of efficiency of the service disciplines. The results also lead to new rules for optimization of the system performance
with respect to the service disciplines at the queues. Further, the exact asymptotic results suggest simple expected waiting-time
approximations for polling models in heavy traffic. Numerical experiments show that the accuracy of the approximations is
excellent for practical heavy-traffic scenarios.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
13.
Mathematical models with stage structures are proposed to describe the process of awareness, evaluation and decision-making. First, a system of ordinary differential equations is presented that incorporates the awareness stage and the decision-making stage. If the adoption rate is bilinear and imitations are dominant, we find a threshold above which innovation diffusion is successful. Further, if the adoption rate has a higher nonlinearity, it is shown that there exist bistable equilibria and a region such that an innovation diffusion is successful inside and is unsuccessful outside. Secondly, a model with a time delay is proposed that includes an evaluation stage of a product. It is proved that the system exhibits stability switches. The bifurcation direction of equilibria is also discussed. 相似文献
14.
15.
In this paper, the Leslie predator-prey system with two delays is studied. The stability of the positive equilibrium is discussed by analyzing the associated characteristic transcendental equation. The direction and stability of the bifurcating periodic solutions are determined by applying the center manifold theorem and normal form theory. The conditions to guarantee the global existence of periodic solutions are given. 相似文献
16.
Jiang Wei 《Journal of Mathematical Analysis and Applications》2004,297(1):305-316
The eigenvalue and the stability of singular differential systems with delay are considered. Firstly we investigate some properties of the eigenvalue, then give the exact exponential estimation for the fundamental solution, and finally discuss the necessary and sufficient condition of uniform asymptotic stability. 相似文献
17.
In this paper, by means of the method of upper and lower solutions and monotone iterative technique, the existence of maximal and minimal solutions of the boundary value problems for first order impulsive delay differential equations is established. 相似文献
18.
Stability and bifurcation in a delayed predator-prey system with Beddington-DeAngelis functional response 总被引:1,自引:0,他引:1
Zhihua Liu 《Journal of Mathematical Analysis and Applications》2004,296(2):521-537
We consider a delayed predator-prey system with Beddington-DeAngelis functional response. The stability of the interior equilibrium will be studied by analyzing the associated characteristic transcendental equation. By choosing the delay τ as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay τ crosses some critical values. The direction and stability of the Hopf bifurcation are investigated by following the procedure of deriving normal form given by Faria and Magalhães. An example is given and numerical simulations are performed to illustrate the obtained results. 相似文献
19.
§ 1. IntroductionRecently ,thedifferentialequationswithdeviatingargumentswereusuallydiscussed(see[1 ],[4],[5 ]) .In [1 ],AGARWALRPandO’REGANDconsideredequationy″(t) =f(t,y(t) ,y(σ(t) ) ) , a.e .t∈ [0 ,1 ]y(t) =ψ(t) , t∈ [-r ,0 ]y( 1 ) =a ,( )andtheydiscussedtheexistenceofatleastonesolutionforequation ( ) .Inthispaper ,weconsideramoregeneralequation-x″(t) =f(t ,xt) , t∈ [0 ,1 ]x(t) =ψ(t) , t∈ ( -∞ ,0 ]x( 0 ) =x( 1 ) =0 ,( 1 .1 )andsomeexistencetheor… 相似文献
20.