Browsing Waterloo Research by Author "Campbell, Sue Ann"
Now showing items 1-16 of 16
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Dynamics of a Diffusive Nutrient-Phytoplankton-Zooplankton Model with Spatio-temporal Delay
Tao, Yiwen; Campbell, Sue Ann; Poulin, Francis J. (SIAM, 2021-01)We study a diffusive nutrient-phytoplankton-zooplankton (NPZ) model with spatio-temporal delay. The closed nature of the system allows the formulation of a conservation law of biomass that governs the ecosystem. We advance ... -
The Effect of Input Signals Time-Delay on Stabilizing Traffic with Autonomous Vehicles
Al-Darabsah, Isam; Al Janaideh, Mohammad; Campbell, Sue Ann (IEEE, 2021-05)This paper extends the results in [1] considering time delays in Standard Car Following models (CFMs). In [1], connected vehicles are characterized with CFMs models and controlled using linear string analysis to stabilize ... -
Hysteresis bifurcation and application to delayed FitzHugh-Nagumo neural systems
Chen, Liang; Campbell, Sue Ann (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
Al-Darabsah, Islam; Chen, Liang; Nicola, Wilten; Campbell, Sue Ann (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 ... -
M-current induced Bogdanov–Takens bifurcation and switching of neuron excitability class
Al-Darabsah, Isam; Campbell, Sue Ann (Springer, 2021-02-15)In this work, we consider a general conductance-based neuron model with the inclusion of the acetycholine sensitive, M-current. We study bifurcations in the parameter space consisting of the applied current Iapp, the maximal ... -
Mean field analysis gives accurate predictions of the behaviour of large networks of sparsely coupled and heterogeneous neurons
Nicola, Wilten; Njap, Felix; Ferguson, Katie; Skinner, Frances; Campbell, Sue Ann (BioMed Central, 2014-07-21)Large networks of integrate-and-fire (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 ... -
Mean-field models for heterogeneous networks of two-dimensional integrate and fire neurons
Nicola, Wilten; Campbell, Sue Ann (Frontiers Media, 2017-12-27)We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential ... -
Nonsmooth Bifurcations of Mean Field Systems of Two-Dimensional Integrate and Fire Neurons
Nicola, Wilten; Campbell, Sue Ann (Society for Industrial and Applied Mathematics, 2016)Mean field systems have recently been derived that adequately predict the behaviors of large networks of coupled integrate-and-fire neurons [W. Nicola and S.A. Campbell, J. Comput. Neurosci., 35 (2013), pp. 87-108]. The ... -
Normalized Connectomes Show Increased Synchronizability with Age through Their Second Largest Eigenvalue
Nicola, Wilten; Campbell, Sue Ann (Society for Industrial and Applied Mathematics, 2021-01)The synchronization of different brain regions is widely observed under both normal and pathological conditions, such as epilepsy. However, the relationship between the dynamics of these brain regions, the connectivity ... -
An Npz Model With State-Dependent Delay Due To Size-Structure In Juvenile Zooplankton
Kloosterman, Matt; Campbell, Sue Ann; Poulin, Francis J. (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 nutrient-phytoplankton-zooplankton (NPZ) model that includes size structure in the juvenile ... -
One-Dimensional Population Density Approaches To Recurrently Coupled Networks Of Neurons With Noise
Nicola, Wilten; Ly, Cheng; Campbell, Sue Ann (Society for Industrial and Applied Mathematics, 2015)Mean-field systems have been previously derived for networks of coupled, two-dimensional, integrate-and-fire neurons such as the Izhikevich, adapting exponential, and quartic integrate-and-fire, among others. Unfortunately, ... -
A Phase Model with Large Time Delayed Coupling
Al-Darabsah, Islam; Campbell, Sue Ann (Elsevier, 2020-10)We consider two identical oscillators with weak, time delayed coupling. We start with a general system of delay differential equations then reduce it to a phase model. With the assumption of large time delay, the resulting ... -
Phase models and clustering in networks of oscillators with delayed coupling
Campbell, Sue Ann; Wang, Zhen (Elsevier, 2017-09-19)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 ... -
Spatially localized cluster solutions in inhibitory neural networks
Ryu, Hwayeon; Miller, Jennifer; Teymuroglu, Zeynep; Wang, Xueying; Booth, Victoria; Campbell, Sue Ann (Elsevier, 2021-06)Neurons in the inhibitory network of the striatum display cell assembly firing patterns which recent results suggest may consist of spatially compact neural clusters. Previous computational modeling of striatal neural ... -
Stability of Connected Autonomous Vehicle Networks with Commensurate Time Delays
Al-Darabsah, Isam; Al Janaideh, Mohammad; Campbell, Sue Ann (IEEE, 2021-05)In this paper, we study the stability of Connected Autonomous Vehicle Networks (CAVN) with commensurate time delays under the assumption that communication time delays increase as the distance between the vehicles increases. ... -
Stability, bifurcation and phase-locking of time-delayed excitatory-inhibitory neural networks
Ryu, Hwayeon; Campbell, Sue Ann (AIMS Press, 2020-11)We study a model for a network of synaptically coupled, excitable neurons to identify the role of coupling delays in generating different network behaviors. The network consists of two distinct populations, each of which ...