18 citations · 61 across the 13 of their papers we have counts for
14 papers
Stability of Phase-locked States of Weakly Coupled Izhikevich Neurons
XinYe Cheng, Sue Ann Campbell
The Izhikevich model is a computationally efficient neuron model that can exhibit a wide range of firing patterns observed in the brain. However, it is a discontinuous dynamical sy…
Exact mean-field models for spiking neural networks with adaptation
Liang Chen, Sue Ann Campbell
Networks of spiking neurons with adaption have been shown to be able to reproduce a wide range of neural activities, including the emergent population bursting and spike synchrony…
Hysteresis bifurcation and application to delayed Fitzhugh-Nagumo neural systems
Liang Chen, Sue Ann Campbell
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…
M-current Induced Bogdanov-Takens Bifurcation and Switching of Neuron Excitability Class
Isam Al-Darabsah, Sue Ann Campbell
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 consist…
Normalized Connectomes Show Increased Synchronizability with Age Through Their Second Largest Eigenvalue
Wilten Nicola, Sue Ann Campbell
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…
A Phase Model with Large Time Delayed Coupling
Isam Al-Darabsah, Sue Ann Campbell
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 ass…
Chaos in Homeostatically Regulated Neural Systems
Wilten Nicola, Peter Hellyer, Sue Ann Campbell +1
Low-dimensional yet rich dynamics often emerge in the brain. Examples include oscillations and chaotic dynamics during sleep, epilepsy, and voluntary movement. However, a general m…
Geometric Analysis of Synchronization in Neuronal Networks with Global Inhibition and Coupling Delays
Hwayeon Ryu, Sue Ann Campbell
We study synaptically coupled neuronal networks to identify the role of coupling delays in network's synchronized behaviors. We consider a network of excitable, relaxation oscillat…
Stability in a scalar differential equation with multiple, distributed time delays
Sue Ann Campbell, Israel Ncube
We consider a linear scalar delay differential equation (DDE), consisting of two arbitrary distributed time delays. We formulate necessary conditions for stability of the trivial s…
Phase models and clustering in networks of oscillators with delayed coupling
Sue Ann Campbell, Zhen Wang
We consider a general model for a network of oscillators with time delayed, circulant coupling. We use the theory of weakly coupled oscillators to reduce the system of delay differ…
An NPZ Model with State-Dependent Delay due to Size-Structure in Juvenile Zooplankton
M. Kloosterman, S. A. Campbell, F. J. Poulin
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 tha…
One-Dimensional Population Density Approaches to Recurrently Coupled Networks of Neurons with Noise
Wilten Nicola, Cheng Ly, Sue Ann Campbell
Mean-field systems have been previously derived for networks of coupled, two-dimensional, integrate-and-fire neurons such as the Izhikevich, adapting exponential (AdEx) and quartic…
Non-smooth Bifurcations of Mean Field Systems of Two-Dimensional Integrate and Fire Neurons
Wilten Nicola, Sue Ann Campbell
Mean-field systems have been recently derived that adequately predict the behaviors of large networks of coupled integrate-and-fire neurons [14]. The mean-field system for a networ…
Mean-Field Models for Heterogeneous Networks of Two-Dimensional Integrate and Fire Models
Wilten Nicola, Sue Ann Campbell
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 inc…