Applied Mathematics
This is the collection for the University of Waterloo's Department of Applied Mathematics .
Research outputs are organized by type (eg. Master Thesis, Article, Conference Paper).
Waterloo faculty, students, and staff can contact us or visit the UWSpace guide to learn more about depositing their research.
Recent deposits

Linearized Stability of Partial Differential Equations with Application to Stabilization of the KuramotoSivashinsky Equation
(Society for Industrial and Applied Mathematics, 20180105)Linearization is a useful tool for analyzing the stability of nonlinear differential equations. Unfortunately, the proof of the validity of this approach for ordinary differential equations does not generalize to all ... 
The forest transition and ecological thresholds: resilience, recovery, and predictions
(University of Waterloo, 20180119)A central topic in modeling land use change is to understand the forest transition from deforestation to net reforestation. Agricultural land use change is the main driver of this phenomenon; classically, agricultural ... 
WellPosedness of Boundary Control Systems
(Society for Industrial and Applied Mathematics, 20030101)Continuity of the input/output map for boundary control systems is shown through the system transfer function. Our approach transforms the question of continuity of the input/output map of a boundary control system to ... 
Stability and Control of Caputo Fractional Order Systems
(University of Waterloo, 20180108)As pointed out by many researchers in the last few decades, differential equations with fractional (noninteger) order differential operators, in comparison with classical integer order ones, have apparent advantages in ... 
Efficient Finitedifference Methods for Sensitivity Analysis of Stiff Stochastic Discrete Models of Biochemical Systems
(University of Waterloo, 20171207)In the study of Systems Biology it is necessary to simulate cellular processes and chemical reactions that comprise biochemical systems. This is achieved through a range of mathematical modeling approaches. Standard methods ... 
Zero Dynamics for PortHamiltonian Systems
(20171119)The zero dynamics of infinitedimensional systems can be difficult to characterize. The zero dynamics of boundary control systems are particularly problematic. In this paper the zero dynamics of portHamiltonian systems ... 
Efficient electrochemical model for lithiumion cells
(20170912)Lithiumion batteries are used to store energy in electric vehicles. Physical models based on electrochemistry accurately predict the cell dynamics, in particular the state of charge. However, these models are nonlinear ... 
Phase models and clustering in networks of oscillators with delayed coupling
(Elsevier, 20170919)We consider a general model for a network of oscillators with time delayed coupling where the coupling matrix is circulant. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations ... 
The Early Universe: New Aspects of Cuscuton Theory, Modified Dispersion Relations and Pulsar Constraints on Vacuum Noise
(University of Waterloo, 20171026)The modern cosmology started blossoming in the early 1900s, with the theoretical framework provided by Einstein's general relativity. Soon after that, with observational discoveries such as expansion of cosmos by Hubble ... 
Nonlinear Preconditioning Methods for Optimization and ParallelInTime Methods for 1D Scalar Hyperbolic Partial Differential Equations
(University of Waterloo, 20171018)This thesis consists of two main parts, part one addressing problems from nonlinear optimization and part two based on solving systems of time dependent differential equations, with both parts describing strategies for ... 
Nonlinear Interactions between Internal Wave Beams: Beyond the Traditional Approximation.
(University of Waterloo, 20170922)The problem of nonlinear interactions of internal waves is solved using smallamplitude expansions beyond the traditional approximation; that is the horizontal component of the Earth’s rotation vector is included in our ... 
Mean field analysis gives accurate predictions of the behaviour of large networks of sparsely coupled and heterogeneous neurons
(BioMed Central, 20140721)Large networks of integrateandfire (IF) model neurons are often used to simulate and study the behaviour of biologically realistic networks. However, to fully study the large network behaviour requires an exploration of ... 
Meanfield models for heterogeneous networks of twodimensional integrate and fire neurons
(Frontiers Media, 20171227)We analytically derive meanfield models for alltoall coupled networks of heterogeneous, adapting, twodimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential ... 
OneDimensional Population Density Approaches To Recurrently Coupled Networks Of Neurons With Noise
(Society for Industrial and Applied Mathematics, 2015)Meanfield systems have been previously derived for networks of coupled, twodimensional, integrateandfire neurons such as the Izhikevich, adapting exponential, and quartic integrateandfire, among others. Unfortunately, ... 
Nonsmooth Bifurcations of Mean Field Systems of TwoDimensional Integrate and Fire Neurons
(Society for Industrial and Applied Mathematics, 2016)Mean field systems have recently been derived that adequately predict the behaviors of large networks of coupled integrateandfire neurons [W. Nicola and S.A. Campbell, J. Comput. Neurosci., 35 (2013), pp. 87108]. The ... 
An Npz Model With StateDependent Delay Due To SizeStructure In Juvenile Zooplankton
(Society for Industrial and Applied Mathematics, 2016)The study of planktonic ecosystems is important as they make up the bottom trophic levels of aquatic food webs. We study a closed nutrientphytoplanktonzooplankton (NPZ) model that includes size structure in the juvenile ... 
The Relation between Polygonal Gravity and 3D Loop Quantum Gravity
(University of Waterloo, 20170913)In this thesis, we explore the relation between ’t Hooft polygonal gravity and loop quantum gravity (LQG)  two models of discrete gravity in 2+1 dimensions. While the relation between the two theories has been studied ... 
Clustering behaviour in networks with time delayed alltoall coupling
(University of Waterloo, 20170830)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 ... 
On Perturbative Methods in Spectral Geometry
(University of Waterloo, 20170828)The goal of spectral geometry is to establish how much information about the geometry of compact Riemannian manifolds is contained in the spectra of natural differential operators, especially Laplacians, defined on them. ... 
Impulsive Control of Dynamical Networks
(University of Waterloo, 20170825)Dynamical networks (DNs) consist of a large set of interconnected nodes with each node being a fundamental unit with detailed contents. A great number of natural and manmade networks such as social networks, food networks, ...