FLIP AND N-S BIFURCATION BEHAVIOR OF A PREDATOR-PREY MODEL WITH PIECEWISE CONSTANT ARGUMENTS AND TIME DELAY

In this paper, the stability and bifurcation behaviors of a predator-prey model with the piecewise constant arguments and time delay are investigated. Technical approach is fully based on Jury criterion and bifurcation theory. The interesting point is that the model will produce two different branches by limiting branch parameters of different intervals. Besides, image simulation is also given.

Almost Periodic Solutioiis of Neutral Differential Difference Equations with Piecewise Constant Arguments

In this paper,we study the existence of almost periodic solutions of neutral differential difference equations with piecewise constant arguments via difference equation methods.

Weighted Pseudo Almost Periodic Solutions of N-th Order Neutral Differential Equations with Piecewise Constant Arguments

In this work, we present some existence theorems of weighted pseudo almost periodic solutions for N-th order neutral differential equations with piecewise constant argument by means of weighted pseudo almost periodic solutions of relevant difference equations.

Multiple bifurcations in an early brain tumor model with piecewise constant arguments

In this paper, a differential equation with piecewise constant arguments modeling an early brain tumor growth is considered. The discretization process in the interval t ∈ [n, n＋1） leads to two-dimensional discrete dynamical system. By using the Schur-Cohn criterion, stability conditions of the positive equilibrium point of the system are obtained. Choosing appropriate bifurcation parameter, the existence of Neimark-Sacker and flip bifurcations is verified. In addition, the direction and stability of the Neimark-Sacker and flip bifurcations are determined by using the normal form and center manifold theory. Finally, the Lyapunov exponents are numerically computed to characterize the complexity of the dynamical behaviors of the system.

NONLINEAR BOUNDARY VALUE PROBLEMS FOR FIRST ORDER DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENTS

The authors employ the method of upper and lower solutions coupled with the monotone iterative technique to obtain some results of existence and un-iqueness for nonlinear boundary value problem of differential equations with piecewise constant arguments.

NECESSARY AND SUFFICIENT CONDITIONS FOR THE OSCILLATION OF A DELAY LOGISTIC EQUATION WITH CONTINUOUS AND PIECEWISE CONSTANT ARGUMENTS

In this paper, we obtain some necessary and sufficient conditions for the oscillation of all positive solutions of a delay Logistic equation with continuous and piecewise constant arguments about the positive equilibrium.

ASYMPTOTIC EQUIVALENCE OF ALTERNATELY ADVANCED AND DELAYED DIFFERENTIAL SYSTEMS WITH PIECEWISE CONSTANT GENERALIZED ARGUMENTS

In this paper, we investigate the existence, uniqueness and the asymptotic equiv- alence of a linear system and a perturbed system of differential equations with piecewise alternately advanced and retarded argument of generalized type （DEPCAG）. This is based in the study of an equivalent integral equation with Cauchy and Green matrices type and in a solution of a DEPCAG integral inequality of Gronwall type. Several examples are also given to show the feasibility of results.

ON THE LASOTA-WAZEWSKA MODEL WITH PIECEWISE CONSTANT ARGUMENT

In this article, a delay differential equation with piecewise constant argument is considered; the existence and global attractivity condition of almost periodic solution and quasi-periodic solution are obtained.

Asymptotically Antiperiodic Solutions for a Nonlinear Differential Equation with Piecewise Constant Argument in a Banach Space

In this paper, we give sufficient conditions for the existence and uniqueness of asymptotically w-antiperiodic solutions for a nonlinear differential equation with piecewise constant argument in a Banach space when w is an integer. This is done using the Banach fixed point theorem. An example involving the heat operator is discussed as an illustration of the theory.

A Set of Almost Automorphic Functions and Applications

For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-almost automorphic functions, we give sufficient conditions of the existence and uniqueness of almost automorphic solutions of a differential equation with a piecewise constant argument of generalized type. This is done using the Banach fixed point theorem.

Global Stability in a Differential Equation with Piecewisely Constant Arguments

In this paper we consider the differential equation with piecewisely constant arguments where ['] -denotes the greates integer function, r(t) E C([0,+∞),(0, +∞)),Pi ∈ [0, +∞)(i = 1, 2,''' , m), with Pm > 0, we establish some new sufficient conditions for an arbitrary solution N(t) to satisfy the initial conditions of the form N(0) = NO > 0 and N(-j) = N-j ≥ 0,j = 1, 2, ., m, to converge to the positive equilibrium N* as t →∞.

STABILITY IN DIFFERENTIAL EQUATIONS WITH CONTINUOUS AND PIECEWISE CONSTANT ARGUMENTS

Consider the delay differential equation with continuous and piecewise constant argumentswhere [·] denotes the greatest integer function. We obtain sufficient conditions for thezero solution of (1) to be (asymptotically) stable.1991 Mathematics Subject Classification: 39A12.

PSEUDO ALMOST PERIODIC SOLUTIONS OF DIFFERENTIAL EQUATIONS WITHPIECEWISE CONSTANT ARGUMENT

The authors discuss the existence of pseudo almost periodic solutions of differential equations with piecewise constant argument by means of introducing new concept, pseudo almost periodic sequence.

Pseudo almost periodic solutions for the systems of differential equations with piecewise constant argument [t]

In this paper, we investigate the existence and uniqueness of new almost periodic type solutions, so-called pseudo almost periodic solutions for the systems of differential equations with piecewise constant argument by means of introducing the notion of pseudo almost periodic vector sequences.

Pseudo Almost Periodic Solutions of a Singularly Perturbed Differential Equation with Piecewise Constant Argument

Under suitable assumptions, the existence and the uniqueness of the pseudo-almost periodic solution for a singularly perturbed differential equation with piecewise constant argument are obtained. In addition, the stability properties of these solutions are characterized by the construction of manifolds of initial data.

The Existence of Pseudo-almost Periodic Solutions of Third-order Neutral Differential Equations with Piecewise Constant Argument

In this paper, we present some existence theorems for pseudo-almost periodic solutions of differential equations with piecewise constant argument by means of pseudo-almost periodic solutions of relevant difference equations.

A Spectrum Relation of Almost Periodic Solution of Second Order Scalar Functional Differential Equations with Piecewise Constant Argument

In this paper, the spectrum relation of almost periodic solution for the equation （x（t） ＋px（t - 1））＂ = qx（[t]） ＋ f（Q is investigated. Although this has been discussed in an article, some counterexamples are constructed to show that some part of the spectrum inclusion in that article is not correct. The key point which causes such problem is found out. A new statement is formulated and proved.

A New Almost Periodic Type Solution of First Order Neutral Delay Differential Equations with Piecewise Constant Argument

In this paper,we introduce a new class of ergodic sequences,pseudo almost periodic sequences,and study the existence of pseudo almost periodic sequences to difference equations.On the basis of these,we investigate the existence of pseudo almost periodic solutions for neutral delay differential equations with piecewise constant argument, d/(dt)(y(t)+py(t-1))=qy(2[(t+1)/2])+g(t,y(t),([t])).

ON ALMOST PERIODIC SOLUTIONS TO THIRD-ORDER NEUTRAL DELAY-DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT

We present some conditions for the existence and uniqueness of almost periodic solutions to third order neutral delay-differential equations with piecewise constant.

LINEARIZED OSCILLATIONS OF DELAY DIFFERENTIAL EQUATIONS AND APPLICATIONS

The necessary and sufficient conditions for the oscillations of every solution of the nonlinear delay equation (t)+f(x(t-l))+g(x( t-k ))=0 are oblained.