Publications

Journal Articles

• 1. Allan R. Willms, 2024. Resonantly Forced ODEs and Repeated Roots, SIAM Review, 64 (1), pp. 149-160. doi=10.1137/23M1545148.

  2. Kolja L. Kypke, William F. Langford, Gregory M. Lewis, Allan R. Willms, 2022. Climate Bifurcations in a Schwarzschild Equation Model of the Arctic Atmosphere, Nonlinear Processes in Geophysics, 29, pp. 219-239, doi=10.5194/npg-29-219-2022.

  3. Chien Hsien Kitty Yang, Shane W. Bateman, Xiu Ting Yiew, Allan R. Willms, 2022. Validation of 3-dimensional mathematical computation of feline bladder volume using ultrasonographic orthogonal bladder images, Canadian Journal of Veterinary Research, 86(3), pp. 200-217..

  4. Connor Gregor, Daniel Ashlock, Allan R. Willms, 2021. The Algebraic Solvability of the Novel Lamplighter Puzzle, ICGA Journal, 43, pp. 203-225, doi=10.3233/ICG-210195.

  5. Allan R. Willms, 2021. Uniform Sampling on the Standard Simplex, Missouri Journal of Mathematical Sciences, 33 (1), pp. 119-124.

  6. Kolja L. Kypke, William F. Langford, Allan R. Willms, 2020. Anthropocene Climate Bifurcation, Nonlinear Processes in Geophysics 27, pp. 391-409, doi=10.5194/npg-27-391-2020.

  7. Andrew Skelton, Allan R. Willms, 2020. Parameter Range Reduction from Partial Data in Systems of Differential Equations, Journal of Computational and Applied Mathematics 372, p. 112698, doi=10.1016/j.cam.2019.112698.

  8. Mona Ghwila, Allan R. Willms, 2019. A Physiologically-Structured Fish Population Model with Size-Dependent Foraging, Mathematical Biosciences, 315, pp. 108233, doi=10.1016/j.mbs.2019.108233.

  9. Xiu Ting Yiew, Samantha Clarke, Allan R. Willms, Shane Bateman, 2019. Feasibility of a Novel 3-Dimensional Mathematical Algorithmic Computation of Feline Bladder Volumes Using Point-of-Care Longitudinal and Transverse Cysto-Colic Ultrasonographic Images, Canadian Journal of Veterinary Research, 83, pp. 298-312.

  10. Brady Dortmans, William F. Langford, Allan R. Willms, 2019. An Energy Balance Model for Paleoclimate Transitions, Climate of the Past, 15 (2), pp. 493-520, doi=10.5194/cp-15-493-2019.

  11. Fatima Etbaigha, Allan R. Willms, Zvonimir Poljak, 2018. An SEIR Model of Influenza A Virus Infection and Reinfection within a Farrow-to-Finish Swine Farm, PLoS ONE 13 (9), p. e0202493, doi=10.1371/journal.pone.0202493.

  12. Petko M. Kitanov, Allan R. Willms, 2018. Probability of Escherichia coli Contamination Spread in Ground Beef Production, Mathematical Biosciences & Engineering 15 (4), pp. 1011-1032, doi=10.3934/mbe.2018045.

  13. Allan R. Willms, Petko M. Kitanov, William F. Langford, 2017. Huygens' Clocks Revisted, R. Soc. Open Sci. 4 (170777), doi=10.1098/rsos.170777.

  14. Marianne Wilcox, Allan R. Willms, William F. Langford, 2015. A Model of the Effects of Fluid Variation due to Body Position on Cheyne-Stokes Respiration, Bulletin of Mathematical Biology 77 (3), pp. 488-498, doi=10.1007/s11538-015-0064-x.

  15. Andrew Skelton, Allan R. Willms, 2015. Parameter Range Reduction in Ordinary Differential Equation Models, Journal of Scientific Computing, 62 (2), pp. 517-531, doi=10.1007/s10915-014-9865-6.

  16. Andrew Skelton, Allan R. Willms, 2014. An Algorithm for Continuous Piecewise Linear Bounding of Discrete Time Series Data, BIT. Numerical Mathematics 54 (4), pp. 1155-1169, doi=10.1007/s10543-014-0492-2.

  17. Hanna M. Härdin, Antonios Zagaris, Allan R. Willms, Hans V. Westerhoff, 2013. Clusters of Reaction Rates and Concentrations in Protein Networks such as the Phosphotransferase System, FEBS Journal 281 (2), pp. 531-548.

  18. Petko Kitanov, William F. Langford, Allan R. Willms, 2013. Double Zero Bifurcation with Huygens Symmetry, Dyn. Cont. Disc. & Imp. Sys. A 20 (2), pp. 197-226.

  19. Allan R. Willms, Emily K. Szusz, 2013. Parameter Range Reduction for ODE Models Using Monotonic Discretizations, J. Comput. Appl. Math. 247, pp. 124-151.

  20. Petko Kitanov, William F. Langford, Allan R. Willms, 2013. Double Hopf Bifurcation with Huygens Symmetry, SIAM J. App. Dyn. Syst. 12 (1), pp. 126-174.

  21. Emily K. Szusz, Allan R. Willms, 2010. A Linear Time Algorithm for Near Minimax Continuous Piecewise Linear Representations of Discrete Data, SIAM J. Sci. Comput. 32 (5), pp. 2584-2602, doi=10.1137/090769077.

  22. Hong Qu, Simon X. Yang, Allan R. Willms, Zhang Yi, 2009. Real-time Robot Path Planning Based on a Modified Pulse Coupled Neural Network Model, IEEE Trans. Neur. Net. 20 (11), pp. 1724-1739.

  23. Allan R. Willms, 2009. Bounding Data with a Piecewise Linear Band, SIAM J. Sci. Comput. 31 (3), pp. 2361-2367.

  24. Allan R. Willms, 2008. Analytic Results for the Eigenvalues of Certain Tridiagonal Matrices, SIAM J. Matrix Anal. Appl. 30 (2), pp. 639-656.

  25. Allan R. Willms, Dominic Nelson, 2008. A Geometric Comparison of Hodgkin-Huxley and Multi-State Models, Bull. Math. Biol. 70 (5), pp. 1503-1524.

  26. Raluca Amariei, Allan R. Willms, Chris T. Bauch, 2008. The United States and Canada as a Coupled Epidemiological System: An Example from Hepatitis A, BMC Infectious Diseases 8 (23), p. .

  27. Allan R. Willms, Simon X. Yang, 2008. Real-Time Robot Path Planning via the Distance-Propagating Dynamic System with Obstacle Clearance, IEEE Trans. Syst., Man, Cybern. B, Cybern. 38 (3), pp. 884-893.

  28. Allan R. Willms, David M. Green, 2007. Reconstruction of Walleye Exploitation Based on Angler Diary Records and a Model of Predicted Catches, Math. Biosci. 210 (1), pp. 96-120.

  29. Allan R. Willms, 2007. Parameter Range Reduction for ODE Models Using Cumulative Backward Differentiation Formulas, J. Comput. Appl. Math. 203 (1), pp. 87-102.

  30. Allan R. Willms, Paul D. Roughan, Jack A. Heinemann, 2006. Static Recipient Cells as Reservoirs of Antibiotic Resistance During Antibiotic Therapy, Theor. Pop. Biol. 70 (4), pp. 436-451.

  31. Allan R. Willms, Simon X. Yang, 2006. An Efficient Dynamic System for Real-Time Robot Path Planning, IEEE Trans. Syst., Man, Cybern. B, Cybern. 36 (4), pp. 755-766.

  32. Allan R. Willms, 2002. NEUROFIT: Software for Fitting Hodgkin-Huxley Models to Voltage-clamp Data, J. Neurosci. Meth. 121, pp. 139-150.

  33. John Guckenheimer, Allan R. Willms, 2000. Asymptotic Analysis of Subcritical Hopf-homoclinic Bifurcation, Physica D 139, pp. 195-216.

  34. Allan R. Willms, Deborah J. Baro, Ronald M. Harris-Warrick, John Guckenheimer, 1999. An Improved Parameter Estimation Method for Hodgkin-Huxley Models, J. Comput. Neurosci. 6, pp. 145-168.

  35. Deborah J. Baro, Robert M. Levini, Marshall T. Kim, Allan R. Willms, Cathy Cole Lanning, Hilda E. Rodriguez, Ronald M. Harris-Warrick, 1997. Quantitative Single-cell-reverse Transcription-PCR Demonstrates that A-Current Magnitude Varies as a Linear Function of shal Gene Expression in Identified Stomatogastric Neurons, J. Neurosci. 17, pp. 6597-6610.

  36. John Guckenheimer, Ronald M. Harris-Warrick, Jack Peck, Allan R. Willms, 1997. Bifurcation, Bursting, and Spike Frequency Adaptation, J. Comp. Neurosci. 4, pp. 257-277.

  37. Xinzhi Z. Liu, Allan R. Willms, 1996. Impulsive Controllability of Linear Dynamical Systems with Applications to Maneuvers of Spacecraft, Math. Prob. Eng. 2, pp. 277-299.

  38. Allan R. Willms, 1995. An Exact Solution of Stikker's Nonlinear Heat Equation, SIAM J. Appl. Math. 55, pp. 1059-1073.

  39. Xinzhi Z. Liu, Allan R. Willms, 1995. Stability Analysis and Applications to Large Scale Impulsive Systems: A New Approach, Cdn. App. Math. Quart. 3, pp. 419-444.

  40. Xinzhi Z. Liu, Allan R. Willms, 1994. Impulsive Stabilizability of Autonomous Systems, J. Math. Anal. Appl. 187, pp. 17-39.

Refereed conference proceedings

• 1. Kolja L. Kypke, William F. Langford, Nathaniel Nethercott, Allan R. Willms, Topological Climate Change with Permafrost Feedback, in: Dimitrios S. Vlachos (Ed.), RJournal of Physics: Conference Series 1730, International Conference on Mathematical Modelling in the Physical Sciences, 7-10 September, 2020, Tinos, Greece, IOP Publishing, pp. 012090, doi=10.1088/1742-6596/1730/1/012090.

  2. Brady Dortmans, William F. Langford, Allan R. Willms, A Conceptual Model for the Pliocene Paradox, in: D. Marc Kilgour, Herb Kunze, Roman Makarov, Roderick Melnik, Sunny Wang (Eds.), Recent Advances in Mathematical and Statistical Methods for Scientific and Engineering Applications, Springer Nature, AMMCS 2017, Waterloo, Canada, 2018, pp. 339-349, doi=10.1007/978-3-319-99719-3_31.

  3. Andrew Skelton, Allan R. Willms, To a Predictive Model of Pathogen Die-off in Soil Following Manure Application, in: J. Bélair, I. Frigaard I, H. Kunze, R. Makarov, R. Melnik, R. Spiteri (Eds.), Mathematical and Computational Approaches in Advancing Modern Science and Engineering, Springer, AMMCS-CAIMS 2015, Waterloo, Canada, 2016, pp. 309-317, doi=10.1007/978-3-319-30379-6_29.

  4. Marianne Waito, Allan R. Willms, Byram W. Bridle, Scott Walsh, A Mathematical Model of Cytokine Dynamics During a Cytokine Storm, in: J. Bélair, I. Frigaard I, H. Kunze, R. Makarov, R. Melnik, R. Spiteri (Eds.), Mathematical and Computational Approaches in Advancing Modern Science and Engineering, Springer, AMMCS-CAIMS 2015, Waterloo, Canada, 2016, pp. 331-339, doi=10.1007/978-3-319-30379-6_31.

  5. Petko M. Kitanov, Allan R. Willms, Estimating Escherichia coli Contamination Spread in Ground Beef Production Using a Discrete Probability Model, in: J. Bélair, I. Frigaard I, H. Kunze, R. Makarov, R. Melnik, R. Spiteri (Eds.), Mathematical and Computational Approaches in Advancing Modern Science and Engineering, Springer, AMMCS-CAIMS 2015, Waterloo, Canada, 2016, pp. 245-254, doi=10.1007/978-3-319-30379-6_23.

  6. Andrew Skelton, Allan R. Willms, Parameter Range Reduction in ODE Models in the Presence of Partial Data Sets, in: Monica G. Cojocaru, Ilias S. Kotsireas, Roman N. Makarov, Roderick V. N. Melnik, Hasan Shodiev (Eds.), Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science, Vol. 117 of Springer Proceedings in Mathematics & Statistics, Springer, AMMCS 2013, Waterloo, Canada, 2015, pp. 419-424.

  7. Marianne Wilcox, Allan R. Willms, The Effects of Body Fluid on Cheyne-Stokes Respiration, in: Monica G. Cojocaru, Ilias S. Kotsireas, Roman N. Makarov, Roderick V. N. Melnik, Hasan Shodiev (Eds.), Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science, Vol. 117 of Springer Proceedings in Mathematics & Statistics, Springer, AMMCS 2013, Waterloo, Canada, 2015, pp. 495-500.

  8. Allan R. Willms, Emily K. Szusz, Analysis of Monotonic Discretizations for ODE Parameter Estimation, in: Ilias Kotsireas, Roderick Melnik, Brian West (Eds.), Advances in Mathematical and Computational Methods: Addressing Modern Challenges of Science, Technology, and Society, Vol. 1368 of AIP Conference Proceedings, AIP, AMMCS 2011, Waterloo, Canada, 2011, pp. 301-304.

  9. Allan R. Willms, Simon X. Yang, An Extension of the Distance-Propagating Dynamic System for Robot Path Planning to Safe Obstacle Clearance, in: Proceedings of the IEEE International Conference on Robotics and Biomimetics, ROBIO 2006, Kuming, China, 2006, pp. 1396-1401.

  10. Stephen P. Gent, Daniel A. Ashlock, Allan R. Willms, Kenneth M. Bryden, Generalized Thermal Agents with Multiple Boundary Conditions and Three-Dimensional Thermal Agents, in: Proceedings of the 2006 Congress on Evolutionary Computation, Vancouver, Canada, 2006, pp. 10935-10942.

  11. Daniel A. Ashlock, Allan R. Willms, Stephen P. Gent, Kenneth M. Bryden, Rapid Training of Thermal Agents with Gradient Single Parents, in: Proceedings of the Seventh International Conference in Adaptive Computing in Design and Manufacture, 2006, pp. 191-198.

  12. Allan R. Willms, Simon X. Yang, A Simple Yet Efficient Dynamic System for Robot Path Planning, in: Proc. of IEEE Intl. Conf. on Robotics and Biomimetics, ROBIO 2004, Shenyang, China, 2004, pp. 677-682.

  13. Xinzhi Z. Liu, Allan R. Willms, Impulsive Stabilization, in: Xinzhi Z. Liu, David Segel (Eds.), Comparison Methods and Stability Theory, Vol. 162 of Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York, Conference in Waterloo, Canada, 1994, pp. 269-276.

Other refereed contributions

• 1. Allan R. Willms, Videos for: Huygens' Clocks Revisited, Dryad Digital Repository, supplementary Material for “Huygens' Clocks Revisted”, A.R. Willms, P.M. Kitanov, and W.F. Langford, R. Soc. Open Sci., 2017 (August 2017), doi=10.5061/dryad.p4sg5.

  2. Allan R. Willms, Breathing Torus Near Double Hopf Bifurcation, DSWeb Magazine (www.dynamicalsystems.org), Media Gallery Entry (April 2013).

Book Chapters

• 1. John Guckenheimer, Joseph H. Tien, Allan R. Willms, Bifurcations in the Fast Dynamics of Neurons: Implications for Bursting, in: Stephen Coombes, Paul C. Bressloff (Eds.), Bursting: The Genesis of Rhythm in the Nervous System, World Scientific Press, 2005, pp. 91-124.