Browsing Mathematics (Faculty of) by Subject "time delay"
Now showing items 1-5 of 5
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Clustering behaviour in networks with time delayed all-to-all coupling
(University of Waterloo, 2017-08-30)Networks of coupled oscillators arise in a variety of areas. Clustering is a type of oscillatory network behavior where elements of a network segregate into groups. Elements within a group oscillate synchronously, while ... -
Hysteresis bifurcation and application to delayed FitzHugh-Nagumo neural systems
(Elsevier, 2021-08)Hysteresis dynamics has been described in a vast number of biological experimental studies. Many such studies are phenomenological and a mathematical appreciation has not attracted enough attention. In the paper, we explore ... -
The Impact of Small Time Delays on the Onset of Oscillations and Synchrony in Brain Networks
(Frontiers Publishing, 2021-07)The human brain constitutes one of the most advanced networks produced by nature, consisting of billions of neurons communicating with each other. However, this communication is not in real-time, with different communication ... -
Invariant manifold theory for impulsive functional differential equations with applications
(University of Waterloo, 2019-07-03)The primary contribution of this thesis is a development of invariant manifold theory for impulsive functional differential equations. We begin with an in-depth analysis of linear systems, immersed in a nonautonomous ... -
Stability analysis by contraction principle for impulsive systems with infinite delays
(Elsevier, 2020-03)This paper studies a class of quasi-linear impulsive systems of functional differential equations with infinite time delay. By employing the contraction principle, several criteria on uniform stability and asymptotic ...