Related papers: DDE-BIFTOOL Manual - Bifurcation analysis of delay…
Recent work in [53, 54] by the authors on periodic center manifolds and normal forms for bifurcations of limit cycles in delay differential equations (DDEs) motivates the derivation of explicit computational formulas for the critical normal…
The mathematical - numerical analysis of a discrete dynamical model with two independent delays was performed. Such model may describe a continuous system with delays that have real rational number values. Applicable characteristic…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…
We describe the algorithms used in the Matlab continuation and bifurcation package pde2path for Hopf bifurcation and continuation of branches of periodic orbits in systems of PDEs in 1, 2, and 3 spatial dimensions, including the computation…
Pseudospectral approximation provides a means to approximate the dynamics of delay differential equations (DDE) by ordinary differential equations (ODE). This article develops a computer-aided algorithm to determine the distance between the…
This paper develops a computational method for studying stable/unstable manifolds attached to periodic orbits of differential equations. The method uses high order Chebyshev-Taylor series approximations in conjunction with the…
In this paper we present a general approach to rigorously validate Hopf bifurcations as well as saddle-node bifurcations of periodic orbits in systems of ODEs. By a combination of analytic estimates and computer-assisted calculations, we…
pde2path is a free and easy to use Matlab continuation/bifurcation package for elliptic systems of PDEs with arbitrary many components, on general two dimensional domains, and with rather general boundary conditions. The package is based on…
Dynamics in delayed differential equations (DDEs) is a well studied problem mainly because DDEs arise in models in many areas of science including biology, physiology, population dynamics and engineering. The change of the nature in the…
The Fault Detection and Isolation Tools (FDITOOLS) is a collection of MATLAB functions for the analysis and solution of fault detection and model detection problems. The implemented functions are based on the computational procedures…
We study the two state model which describes the balance equation for carbon dioxide and oxygen. These are nonlinear parameter dependent and because of the transport delay in the respiratory control system, they are modeled with delay…
We describe how some differential geometric bifurcation problems can be treated with the MATLAB continuation and bifurcation toolbox pde2path. The basic setup consists in solving the PDEs for the normal displacement of an immersed surface…
In this paper we prove that periodic boundary-value problems (BVPs) for delay differential equations are locally equivalent to finite-dimensional algebraic systems of equations. We rely only on regularity assumptions that follow those of…
Dynamics in delayed differential equations (DDEs) is a well studied problem mainly because DDEs arise in models in many areas of science including biology, physiology, population dynamics and engineering. The change of nature in the…
We present algorithms and their implementation to compute limit cycles and their isochrons for state-dependent delay equations (SDDE's) which are perturbed from a planar differential equation with a limit cycle. Note that the space of…
ISIM1s consists of a few MATLAB functions and a script that can be used to derive stabilizing impulsive controllers for delay differential equations. This document serves as both a manual and tutorial on the functionality of the ISIM1s…
We study a scalar DDE with two delayed feedback terms that depend linearly on the state. The associated constant-delay DDE, obtained by freezing the state dependence, is linear and without recurrent dynamics. With state dependent delay…
We consider a delay differential equation that occurs in the study of chronic myelogenous leukemia. After shortly reminding some previous results concerning the stability of equilibrium solutions, we concentrate on the study of stability of…
A recent work by the authors on the existence of a periodic smooth finite-dimensional center manifold near a nonhyperbolic cycle in delay differential equations motivates the derivation of periodic normal forms. In this paper, we prove the…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…