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.

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.

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.

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.

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])).

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 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.

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.

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.

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.

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.

Complex dynamics of COVID-19 mathematical model on Erdos-Rényi network

In this study,a conformable fractional order Lotka-Volterra predator-prey model that describes the COVID-19 dynamics is considered.By using a piecewise constant approximation,a discretization method,which transforms the conformable fractional-order differential equation into a difference equation,is introduced.Algebraic conditions for ensuring the stability of the equilibrium points of the discrete system are determined by using Schur-Cohn criterion.Bifurcation analysis shows that the discrete system exhibits Neimark-Sacker bifurcation around the positive equilibrium point with respect to changing the parameter d and e.Maximum Lyapunov exponents show the complex dynamics of the discrete model.In addition,the COVID-19 mathematical model consisting of healthy and infected populations is also studied on the Erdos Rényi network.If the coupling strength reaches the critical value,then transition from nonchaotic to chaotic state is observed in complex dynamical networks.Finally,it has been observed that the dynamical network tends to exhibit chaotic behavior earlier when the number of nodes and edges increases.All these theoretical results are interpreted biologically and supported by numerical simulations.

Green's Function for Periodic Solutions in Alternately Advanced and Delayed Differential Systems

In this paper we investigate the existence of the periodic solutions of a nonlinear differential equation with a general piecewise constant argument,in short DEPCAG,that is,the argument is a general step function.We consider the critical case,when associated linear homogeneous system admits nontrivial periodic solutions.Criteria of existence of periodic solutions of such equations are obtained.In the process we use the Green?s function for periodic solntions and convert the given DEPCAG into an equivalent integral equation.Then we construct appropriate mappings and employ Krasnoselskii's fixed point theorem to show the existence of a periodic solution of this type of nonlinear differential equations.We also use the contraction mapping principle to show the existence of a unique periodic solution.Appropriate examples are given to show the feasibility of our results.