Results 251 to 260 of about 2,013,353 (284)

New Results on Linearization of Differential Equations with Piecewise Constant Argument

Qualitative Theory of Dynamical Systems, 2020
The following nonlinear system with piecewise constant argument of generalized type (DEPCAGs) is considered: \begin{align*} x'(t) &= A(t)x(t) + A_0(t)x(\gamma(t)) + f(t, x(t), x(\gamma(t))),\\ y'(t) &= B(t)y(t) + B_0(t)y(\gamma(t)) + g(t, x(t), x(\gamma(t))), \\ z'(t) &= C(t)z(t) + C_0(t)z(\gamma(t)) + \varphi(t, z(t), z(\gamma(t))) + \psi(t, x(t), y(t)
Hai Huang, Yong-Hui Xia
openaire   +2 more sources

Flip and Neimark–Sacker bifurcation in a differential equation with piecewise constant arguments model [PDF]

Journal of Difference Equations and Applications, 2017
In this paper, a differential equation with piecewise constant arguments model that describes a population density of a bacteria species in a microcosm is considered. The discretization process of a differential equation with piecewise constant arguments
Kartal, Şenol
exaly   +1 more source

ON THE LASOTA-WAZEWSKA MODEL WITH PIECEWISE CONSTANT ARGUMENT

Acta Mathematica Scientia, 2006
Abstract 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.
Feng Qiuxiang, Yuan Rong
openaire   +1 more source

Comparison principle and stability of differential equations with piecewise constant arguments

Journal of the Franklin Institute, 2013
Abstract This paper studies systems of nonlinear differential equations with piecewise constant arguments (EPCA). We develop a comparison principle for this system. Then, this result is used to establish some stability properties of the system. As for the stability results we employ the Lyapunov function approach.
Mohamad S. Alwan, Xinzhi Liu, Wei-Chau Xie   +2 more
openaire   +1 more source

The State-Dependent Piecewise Constant Argument

2011
In previous chapters, the differential equations with piecewise constant argument of generalized type (differential equations with piecewise constant arguments) of the form \( {\frac{dx(t)}{dt}} = f(t,x(t),\;x(\beta (t))), \) (6.1) are considered, where β (t) = θ i if θ i ≤ t < θ i+1, i are integers, is an identification function, θ i is a strictly ...
openaire   +1 more source

ALMOST PERIODIC SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT

Analysis, 1996
Differential equations with piecewise constant arguments are considered. Existence of almost periodic solutions of such equations is proved. Nonlinear differential equations of the same type are studied as well.
Yuan, Rong, Hong, Jialin
openaire   +1 more source

Stability analysis of macrophage-tumor interaction with piecewise constant arguments

AIP Conference Proceedings, 2015
This study is based on a tumor growth that is modeled such as {dM(t)dt=M(t)r1(1−α1M(t)−bM〚t〛)−bM(t)A(〚t〛)−d1M(t)M(〚t〛)+E1M(t)A(〚t〛)dA(t)dt=A(t)(bM〚t〛−d2)dT(t)d=T(t)r2(1−β1T(t)−β2T〚t〛)−aT(t)A(〚t〛)+cT(t) where M, A and T denote respectively the concentrations of macrophages, activated macrophages and tumor cells. The parameters α1, α2, k1, k2, β1, β2, d1,
BOZKURT, Fatma, ÖZKÖSE, Fatma
openaire   +2 more sources

Stability Analysis of Impulsive Neural Networks with Piecewise Constant Arguments

Neural Processing Letters, 2017
The global exponential stability problem is considered for a class of impulsive neural networks with piecewise constant arguments in this paper. By employing the Banach fixed point theorem and the Razumikhin-type technique, stability criterion is obtained for the existence, uniqueness and global exponential stability of the periodic solution.
Tianhu Yu, Dengqing Cao
openaire   +2 more sources

Global stability and chaos in a population model with piecewise constant arguments

Applied Mathematics and Computation, 1999
Sufficient conditions are obtained for the global stability of the positive equilibrium of the equation \[ (1)\qquad dx/dt = rx(t)\left\{1-cx(t)-b\sum^\infty_{j=0}c_jx(|t-j|)\right\}, \] where \(r>0\)~, \(c>0\)~, \(d_j\) (~\(j=0,1,2,\cdots\)~) are nonnegative and \(\sum\limits^\infty_{j=0 ...
Pingzhou Liu, K. Gopalsamy
openaire   +3 more sources

Functional Differential Equations with Piecewise Constant Argument

2017
We introduce a new class of functional differential equations with functional response on piecewise constant argument, \({ FDEPCA}\). It contains functional differential equations with continuous time [21, 25, 28, 31] as well as differential equations with piecewise constant argument [1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 22, 22,
openaire   +1 more source