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Delay Differential Equations: Theory, Applications, and New Trends

Call for Papers

Recently, there has been increasing interest related to the theory of delay differential equations. To a large extent, this is due to the realization that delay differential equations are important in applications. New applications that involve delay differential equations continue to arise with increasing frequency in the modeling of diverse phenomena in physics, biology, ecology, and physiology. There is no doubt that some of the recent developments in the theory of delay differential equations have enhanced our understanding of the qualitative behavior of their solutions and have many applications in mathematical biology and other related fields. Both theory and applications of delay differential equations require a bit more mathematical maturity than their ordinary differential equations counterparts. Primarily, this is because the theory of complex variables plays such a large role in analyzing the characteristic equations that arise on linearizing around equilibria.

Time delay dynamical systems are generally described by delay differential equations. The mathematical description of delay dynamical systems will naturally involve the delay parameter in some specified way. This can be in the form of differential equations with delay or difference equations with delay or differential-difference equations with delay or even might include integral forms (integrodifferential equations). A differential equation with delay describing a dynamical system belongs to the class of retarded functional differential equations (also sometimes called retarded differential-difference equations).

A delay differential equation or time delay system that describes some physical process is often called a time delay model of the process. Time delay models are abundant in nature. These models occur in a wide variety of physical, chemical, engineering, economic, and biological systems because many processes include aftereffect phenomena in their inner dynamics. Nonlinear delay dynamical systems have been studied intensely in the recent years in diverse areas of science and technology, particularly in the context of chaotic dynamics.

The main objective of this special issue is to provide an opportunity to study the analytical insights of the delay differential equations, existence and uniqueness of the solutions, boundedness and persistence, oscillatory behavior of the solutions, stability and bifurcation analysis, periodic and quasiperiodic solutions, and numerical investigations of solutions.

We invite authors and researchers to contribute their original research articles as well as review articles.

Potential topics include but are not limited to the following:

  • Development of novel theories or improvement to existing theories on delay differential equations
  • Development of novel numerical approaches for delay differential equations
  • Development of novel time delay models with their analytical or qualitative investigation
  • Stability and bifurcation analysis of time delay models

Authors can submit their manuscripts through the Manuscript Tracking System at

Submission DeadlineFriday, 4 May 2018
Publication DateSeptember 2018

Papers are published upon acceptance, regardless of the Special Issue publication date.

Lead Guest Editor

  • Qamar Din, University of Poonch, Rawalakot, Pakistan

Guest Editors

  • Tzanko Donchev, University of Architecture and Civil Engineering, Sofia, Bulgaria
  • Dimitar Kolev, University of Chemical Technology and Metallurgy, Sofia, Bulgaria
  • Muhammad Ozair, COMSATS Institute of Information Technology, Attock, Pakistan
  • Takasar Hussain, COMSATS Institute of Information Technology, Attock, Pakistan