Publications.

Below is a list of publications. Paywall-free download links to accepted manuscripts, preprints, or publisher versions (if permitted) are provided. Accepted manuscripts might contain small typos or minor errors that were caught during the proofing process, while preprints may contain errors that were subsequently corrected during peer review. If you would like a copy of a final published article (or a preprint to something under review), just send me an email and I will forward one to you.

Last updated: 2023-09-17.
Submitted works
  1. I. Hewage, K.E.M. Church and E.J. Schwartz. Investigating the impact of vaccine hesitancy on an emerging infectious disease: A mathematical and numerical analysis. Submitted September, 2023.
  2. K.E.M. Church, Computer-assisted proofs with deep neural networks​. Submitted February, 2023. (preprint)

Journal publications and refereed conference proceedings
  1. J. Cyranka, K.E.M. Church and J. Lessard. Worrisome Properties of Neural Network Controllers and Their Symbolic Representations. 26th European Conference on Artificial Intelligence (ECAI 2023), Krakow, Poland. (Accepted, preprint)
  2. ​K.E.M. Church and E. Queirolo. Computer-assisted proofs of Hopf bubbles and degenerate Hopf bifurcations. Journal of Dynamics and Differential Equations, 2023. (open access)
  3. Kevin E. M. Church, Olivier Hénot, Phillipo Lappicy, Jean-Philippe Lessard, Hauke Sprink. Periodic orbits in Hořava–Lifshitz cosmologies, General Relativity and Gravitation, 55:2, 2023. (preprint, journal)
  4. K.E.M. Church, Uniqueness of solutions and linearized stability for impulsive differential equations with state-dependent delay. Journal of Differential Equations, Volume 338, 415-400, 2022. (journal, preprint)
  5. K.E.M. Church, Validated integration of differential equations with state-dependent delay. Communications in Nonlinear Science and Numerical Simulation, Volume 115, 106762, 2022. (journal, preprint)
  6. K.E.M. Church and G.W. Duchesne, Rigorous continuation of periodic solutions for impulsive delay differential equations, Applied Mathematics and Computation, 415(15), 126733, 2022. (journal, preprint).
  7. K.E.M. Church and J. Lessard, Rigorous verification of Hopf bifurcations in functional differential equations of mixed type, Physica D: Nonlinear Phenomena, Volume 429, 133072, 2022. (journal, accepted manuscript)
  8. K.E.M. Church and C. Fortin, Computer-assisted methods for analyzing periodic orbits in vibrating gravitational billiards, International Journal of Bifurcation and Chaos, 31(08):2130021, 2021 (preprint, journal)
  9. K.E.M. Church, Analysis of pandemic closing-reopening cycles using rigorous homotopy continuation: a case study with Montreal COVID-19 data, SIAM Journal on Applied Dynamical Systems, 20(2), 745–783, 2021 (accepted manuscript; journal).
  10. K.E.M. Church and X. Liu, ​Invariant manifold-guided impulsive stabilization of delay equations, IEEE Transactions on Automatic Control, Volume 66(12), 2021. (accepted manuscript, journal)
  11. K.E.M. Church, Eigenvalues and delay differential equations: periodic coefficients, impulses and rigorous numerics, Journal of Dynamics and Differential Equations, October 2020 (Download link: accepted manuscript; link: journal).
  12. K.E.M. Church and X. Liu, Cost-effective robust stabilization and bifurcation suppression, SIAM Journal on Control and Optimization, 57 (3), 2240–2268 June 2019. (Download link: published article)
  13. K.E.M. Church and X. Liu, Computation of centre manifolds and some codimension-one bifurcations for impulsive delay differential equations, Journal of Differential Equations, 267 (6), 3852–3921 December 2019. (Download link: accepted manuscript; link: journal)
  14. K.E.M. Church and X. Liu, Analysis of a SIR model with pulse vaccination and temporary immunity: stability, bifurcation and a cylindrical attractor, Nonlinear Analysis: Real World Applications, 50, 240–266 September 2019. (Download link: accepted manuscript; link: journal)
  15. K.E.M. Church and X. Liu, Smooth centre manifolds for impulsive delay differential equations, Journal of Differential Equations, 265 (4), 1696–1759 August 2018. (Download link: accepted manuscript; link: journal)
  16. K.E.M. Church and R.J. Smith?, Continuous approximation of linear impulsive systems and a new form of robust stability,  Journal of Mathematical Analysis and Applications, 457 (1), 616–644 January 2018. (Download link: accepted manuscript)
  17. K.E.M. Church and X. Liu, Bifurcation analysis and application for impulsive systems with delayed impulses, International Journal of Bifurcation and Chaos, 27 (12), 1750186 December 2017. (Download link: accepted manuscript)
  18. K.E.M. Church and X. Liu, Bifurcation of bounded solutions of impulsive differential equations, International Journal of Bifurcation and Chaos, 26 (14), 1650242 December 2016. (Download link: accepted manuscript)
  19. K.E.M. Church and R.J. Smith?, Comparing malaria surveillance with periodic spraying in the presence of insecticide-resistant mosquitoes: Should we spray regularly or based on human infections?, Mathematical Biosciences, 276, 145–163 June 2016. (Download link: accepted manuscript)
  20. ​K.E.M. Church and R.J. Smith?, Existence and uniqueness of solutions of general impulsive extension equations with specification to linear equations, Dynamics of Continuous, Discrete and Impulsive Systems: Series B: Applications and Algorithms, 22, 163-197, 2015. (Download link: accepted manuscript)
  21. K.E.M. Church and R.J. Smith?, Analysis of piecewise-continuous extensions of periodic linear impulsive differential equations with fixed, strictly inhomogeneous impulses, Discrete and Impulsive Systems: Series B: Applications and Algorithms, 21, 101-119, 2014​. (Download link: accepted manuscript)

Research monographs
  1. 1. K.E.M. Church and X. Liu, Bifurcation Theory of Impulsive Dynamical Systems, IFSR International Series in Systems Science and Systems Engineering, Volume 34, Springer Nature, 2021. (Publisher page)

Theses and non-refereed conference proceedings
  1. ​K. Church, Invariant manifold theory for impulsive functional differential equations with applications, Doctoral Thesis, University of Waterloo, 2019. (Link to Waterloo repository)
  2. K.E.M. Church. Linearization and local topological conjugacies for impulsive systems. In: Kilgour, D.M., Kunze, H., Makarov, R., Melnik, R., Wang, X. (Eds.) Recent Advances in Mathematical and Statistics Methods: IV AMMCS International Conference, Waterloo, Canada, August 20-25, 2017.
  3. K.E.M. Church. A new measure of robust stablity for linear ordinary impulsive differential equations. In: Belair, J., Frigaard I., Kunze H., Makarov R., Melnik R., Spiteri R. (Eds.) Mathematical and Computational Approaches in Advancing Modern Science and Engineering, 2016.
  4. K. Church, Applications of impulsive differential equations to the control of malaria outbreaks and introduction to impulse extension equations: a general
    framework to study the validity of ordinary differential equation models with discontinuities in state    , Master's Thesis, University of Ottawa. (Link to uOttawa repository)
 
Non-refereed contributions​
  1. K.E.M. Church, User manual and tutorial for ISIM1s: a tiny MATLAB package for single stage invariant manifold-guided impulsive stabilization of delay equations. Maintained 2019 -- 2021. (Link to: arXiv)