Abstract
In order to understand the dynamics of a second order delay differential equation with a piecewise constant argument, we investigate invariant curves of the derived planar mapping from the equation. All invariant curves are given in this paper.
Highlights
1 Introduction The study of differential equations with piecewise constant argument (EPCA) initiated in [, ]. These equations represent a hybrid of continuous and discrete dynamical systems and combine the properties of both differential and difference equations, they are of importance in control theory and in certain biomedical models [ ]
Its invariant curves of the form y satisfy f (y) g(x)), which leads to the iterative functional equation
By the theory of iterative roots, as shown in [ ], we know ( ) has no real continuous solutions
Summary
The study of differential equations with piecewise constant argument (EPCA) initiated in [ , ]. Wiener and Cooke considered oscillations of the solutions of systems of two differential equations with piecewise constant arguments in [ ]. In this paper all the invariant curves of the planar mapping G are given including the linear and nonlinear ones when g is linear.
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