Browsing Mathematics (Faculty of) by Author "Church, Kevin E. M."
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Bifurcation analysis and application for impulsive systems with delayed impulses
Church, Kevin E.M.; Liu, Xinzhi (World Scientific, 2017-11)In this article, we present a systematic approach to bifurcation analysis of impulsive systems with autonomous or periodic right-hand sides that may exhibit delayed impulse terms. Methods include Lyapunov–Schmidt reduction ... -
Bifurcation of Bounded Solutions of Impulsive Differential Equations
Church, Kevin E. M.; Liu, Xinzhi (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 ... -
Comparing malaria surveillance with periodic spraying in the presence of insecticide-resistant mosquitoes: Should we spray regularly or based on human infections?
Church, Kevin E. M.; Smith, Robert J. (Elsevier, 2016-06-01)There is an urgent need for more understanding of the effects of surveillance on malaria control. Indoor residual spraying has had beneficial effects on global malaria reduction, but resistance to the insecticide poses a ... -
Continuous approximation of linear impulsive systems and a new form of robust stability
Church, Kevin E. M.; Smith, Robert J. (Elsevier, 2018-01-01)The time-scale tolerance for linear ordinary impulsive differential equations is introduced. How large the time-scale tolerance is directly reflects the degree to which the qualitative dynamics of the linear impulsive ... -
Invariant manifold theory for impulsive functional differential equations with applications
Church, Kevin E. M. (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 ... -
Smooth centre manifolds for impulsive delay differential equations
Church, Kevin E. M.; Liu, Xinzhi (Elsevier, 2018-04-16)The existence and smoothness of centre manifolds and a reduction principle are proven for impulsive delay differential equations. Several intermediate results of theoretical interest are developed, including a variation ...