here, a predator-prey model with hassell-varley type functional responses is studied. some sufficient conditions are obtained for the permanence and global asymptotic stability of the system by using comparison theorem and constructing a suitable lyapunov functional. moreover, an example is illustrated to verify the results by simulation.

Many topics and techniques regarding asymptotic centers and asymptotic radius were studied by Edelstein 1 , Bose and Laskar 2 , Downing and Kirk 3 , Goebel and Kirk 4 , and Lan and Webb 5 . Now, We recall that definitions of asymptotic center and asymptotic radius. Let C be a nonempty subset of a Banach space X and {xn} a bounded sequence in X. Consider the functional ra ·, {xn} : X → R defined by

In this paper we discuss on the fixed points of asymptotic contractions and Boyd-Wong type contractions in uniform spaces equipped with an E-distance. A new version ofKirk's fixed point theorem is given for asymptotic contractions and Boyd-Wong type contractions is investigated in uniform spaces.

The equivalent, second equivalent and (simply) modi®ed equations for the implicit midpoint rule are shown to be asymptotically equivalent in the sense that an asymptotic analysis of these equations with the time step size as small parameter yields exactly the same results; for linear problems with constant coecients, they are also equivalent to the original ®nite di€erence scheme. Straightforw...

In order to integrate numerically a well-posed multiscale evolutionary problem such as a Cauchy problem for an ODE system or a PDE system, using time-subcycling techniques consists in splitting the vector field in a fast part and a slow part and taking advantage of this decomposition, for example by integrating the fast equation on a much smaller time step than the slow equation (instead of hav...

We consider the problem of calculating resonance frequencies and radiative losses of an optical resonator. The optical resonator is in the form of a thin membrane with variable dielectric properties. This work provides two very different approaches for doing such calculations. The first is an asymptotic method which exploits the small thickness and high index of the membrane. We derive a limiti...

in this paper we discuss on the fixed points of asymptotic contractions and boyd-wong type contractions in uniform spaces equipped with an e-distance. a new version ofkirk's fixed point theorem is given for asymptotic contractions and boyd-wong type contractions is investigated in uniform spaces.

After a short presentation of the boundary layer method extended to strongly elongated objects by Andronov and Bouche [1], the author develops some techniques for deriving explicit formulas for the asymptotic currents on a strongly elongated object of revolution excited by an electromagnetic plane wave propagating in the paraxial direction. The performance of the different techniques are demons...