Browsing Applied Mathematics by Subject "bifurcation"
Now showing items 1-7 of 7
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Bifurcation of Bounded Solutions of Impulsive Differential Equations
(World Scientific Publishing, 2016-12-30)In this article, we examine nonautonomous bifurcation patterns in nonlinear systems of impulsive differential equations. The approach is based on Lyapunov–Schmidt reduction applied to the linearization of a particular ... -
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 ... -
Collective Dynamics of Large-Scale Spiking Neural Networks by Mean-Field Theory
(University of Waterloo, 2024-05-31)The brain contains a large number of neurons, each of which typically has thousands of synaptic connections. Its functionality, whether function or dysfunction, depends on the emergent collective dynamics arising from the ... -
Detecting and distinguishing transitions in ecological systems: model and data-driven approaches
(University of Waterloo, 2020-01-22)There exists a plethora of systems that have the capacity to undergo sudden transitions that result in a significantly different state or dynamic. Consider the collapse of fisheries, outbreak of disease or transition to a ... -
Dynamics of a Diffusive Nutrient-Phytoplankton-Zooplankton Model with Spatio-temporal Delay
(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 ... -
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 ... -
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 ...