Publications - S.A. Campbell

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Preprints

  1. M. Ahmed and S.A. Campbell. Computational Modelling of Resistance to Hormone-Mediated Remission in Childhood Absence Epilepsy. Preprint
  2. I. Al-Darabsah, S.A. Campbell and B. Rahman. Influence of Large Mean Delay on Distributed Delay Differential Equations Dynamics: Application to a Neural Mass Model. arXiv:2509.05466
  3. K. He, S.A. Campbell and S. Liu. Complex dynamics induced by multiple timescales in a Wilson-Cowan model with homeostatic plasticity.
Journal Articles
  1. M. Ahmed and S.A. Campbell Modelling the effect of allopregnanolone on the resolution of spike-wave discharges. J. Computational Neuroscience 53:115-130. Preprint bioRxiv 2023.07.06547738.
  2. I. Al-Darabsah, S.A. Campbell and B. Rahman. Distributed Delay and Desynchronization in a Neural Mass Model. SIAM J. Applied Dynamical Systems 23(4) (2024). Preprint arXiv 2311.15329.
  3. Y. Tao, S.A. Campbell and J. Ren. The Ananthakrishna Model Under Non-synchronous Perturbation. Acta Mathematicae Applicatae Sinica, English Series 40 (4) (2024) 1078-1097.
  4. L. Chen and S.A. Campbell. Population Dynamics of Networks of Izhikevich Neurons with Global Delayed Coupling. SIAM J. Applied Dynamical Systems. 23(3) (2024) 2293-2322. Prepint arXiv 2310.04596.
  5. I. Al-Darabsah, K.-F. Hsueh, A. Khalil, M. Al Janaideh, S.A. Campbell and D. Kundur Validation of an autonomous vehicle platoons model with time-varying communication delays Chaos, Solitons & Fractals 184 (2024) 114983.
  6. M. Sterpu, C. Roscoreanu, R. Efrem and S.A. Campbell Stability and Bifurcations in a Nutrient-Phytoplankton-Zooplankton Model with Delayed Nutrient Recycling with Gamma Distribution Mathematics 11(13)(2023).
  7. J. Miller, H. Ryu, X. Wang, V. Booth and S.A. Campbell. Patterns of synchronization in 2D networks of inhibitory neurons. Frontiers in Computational Neuroscience 16 (2022). DOI:10..3389/fncom.2022.903883.
  8. L. Chen and S.A. Campbell. Exact mean-field models for spiking neural networks with adaptation J. Computational Neuroscience 50 (2022) 445-469. DOI:10.1007/s10827-022-00825-9. Reprint arXiv.2203.08341.
  9. Y. Tao, S.A. Campbell and F.J. Poulin. Dynamics of a diffusive nutrient-phytoplankton-zooplankton model with spatio-temporal delay. SIAM J. Applied Mathematics 81(6)(2021) 2405-2432.
  10. I. Al-Darabsah, L. Chen, W. Nicola and S.A. Campbell. The impact of small time delays on the onset of oscillations and synchrony in brain networks. Frontiers in Systems Neuroscience 15 (2021) 688517. DOI:10.3389/fnsys.2021.688517.
  11. W. Nicola and S.A. Campbell. Normalized connectomes show increased synchronizability with age through their second largest eigenvalue. SIAM J. Applied Dynamical Systems 20(2) (2021) 1158-1176. 10.1137/20M1370082. arXiv:2007.00079
  12. L. Chen and S.A. Campbell. Hysteresis bifurcation and application to delayed FitzHugh-Nagumo systems. J. Mathematical Analysis and Applications 500(1) (2021) 125151. arXiv:2009.14046
  13. H. Ryu, J. Miller, Z. Teymuroglu, X. Wang, V. Booth and S.A. Campbell. Spatially localized cluster solutions in inhibitory neural networks. Mathematical Biosciences (2021). biorXiv:2020.07.30.229542
  14. I. Al-Darabsah and S.A. Campbell. M-current induced Bogdanov-Takens bifurcation and switching of neuron excitability class. J. Mathematical Neuroscience 11(5) (2021). arXiv:2008.01845
  15. H. Ryu and S.A. Campbell. Stability, bifurcation and phase-locking of time-delayed excitatory-inhibitory neural networks. Mathematical Biosciences and Engineering 17(6) (2020), 7931-7957. biorXiv:2020.08.30.274662
  16. M. Chugunova and S.A. Campbell. Difference population equation with variable Allee effect and periodic carrying capacity. J. Difference Equations and Applications 26(6) (2020), 753-778
  17. I. Al-Darabsah and S.A. Campbell. A phase model with large time delayed coupling. Physica D 411 (2020) 132559. arXiv:1910.034355.
  18. H. Ryu and S.A. Campbell. Geometric analysis of synchronization in neuronal networks with global inhibition and coupling delays. Philosophical Transactions A 377 (2019) 20180129. DOI: 10.1098/rsta.2018.0129. Preprint
  19. Y. Liu, J. Milton and S.A. Campbell. Outgrowing seizures in Childhood Absence Epilepsy: Time delays and bistability. J. Computational Neuroscience 46(2) (2019), 197-209. DOI: 10.1007/s10827-019-00711-x. Preprint. Reprint. Code is available on modelDB
  20. W. Nicola, P. Hellyer, S.A. Campbell and C. Clopath Chaos in homeostatically regulated neural systems CHAOS 28 083104 (2018). DOI: 10.1063/1.5026489. Reprint. arXiv:1801.09997
  21. X. Li, J. Ren, S.A. Campbell, G.S.K. Wolkowicz and H. Zhu. Dynamics of a seasonally forced predator-prey model with nonmonotonic functional response. Dynamics of Discrete and Continuous Systems 23(2) (2018) 785-807.
  22. S.A. Campbell and Z. Wang. Phase models and clustering in networks of oscillators with delayed coupling. Physica D 363 (2018) 44-55. arXiv:1607.05759
  23. Z. Wang and S.A. Campbell. Symmetry, Hopf bifurcation and the emergence of cluster solutions in time delayed neural networks. CHAOS 27(11) (2017) 114316. DOI: 10.1063/1.5006921. Preprint
  24. S.A. Campbell and I. Ncube. Stability in a scalar differential equation with multiple, distributed time delays. J. Mathematical Analysis and Applications 450(2) (2017) 1104-1122. arXiv:1611.00207
  25. M. Kloosterman, S.A. Campbell and F.J. Poulin. An NPZ model with state-dependent delay due to size-structure in juvenile zooplankton. SIAM J. Applied Mathematics 76(2)(2016) 551-577. Reprint
  26. W. Nicola and S.A. Campbell. Non-smooth bifurcations of mean field systems of two-dimensional integrate and fire neurons. SIAM J. Applied Dynamical Systems 15(1) (2016) 391-439. Reprint
  27. K. Ferguson, F. Njap, W. Nicola, F.K. Skinner and S.A. Campbell. Examining the limits of cellular adaptation bursting mechanisms in biologically-based excitatory networks of the hippocampus. J. Computational Neuroscience 39(3) (2015) 289-309. doi: 10.1007/s10827-015-0577-1. Preprint Reprint Simulation code
  28. W. Nicola, C. Ly and S.A. Campbell. One-dimensional population density approaches to recurrently coupled networks of neurons with noise. SIAM J. Applied Mathematics 75(5) (2015) 2333-2360. doi: 10.1137/140995738 Reprint.
  29. M. Kloosterman, S.A. Campbell and F.J. Poulin. A closed NPZ model with delayed nutrient recycling. J. Mathematical Biology 68(4) (2014) 815-850. doi: 10.1007/s00285-013-0646-x. Preprint Reprint
  30. W. Nicola and S.A. Campbell. Mean-field models for heterogeneous networks of two-dimensional integrate and fire neurons. Frontiers in Computational Neuroscience 7 (2013) 184. doi: 10.3389/fncom.2013.00184.
  31. W. Nicola and S.A. Campbell. Bifurcations of large networks of two-dimensional integrate and fire neurons. J. Computational Neuroscience 35(1) (2013) 87-108. doi: 10.1007/s10827-013-0442-z. Preprint Reprint Simulation code
  32. G. Fan, S.A. Campbell, G.S.K. Wolkowicz and H. Zhu. The bifurcation study of 1:2 resonance in a delayed system of two coupled neurons. J. Dynamics Differential Equations 25(1) (2013) 193-216. doi: 10.1007/s10884-012-9279-9. Reprint
  33. M. Dur-e-Ahmad, W. Nicola, S.A. Campbell and F.K. Skinner. Network bursting using experimentally constrained single compartment CA3 hippocampal neuron models with adaptation J. Computational Neuroscience 33(1) (2012) 21-40. Reprint
  34. S.A. Campbell and I. Kobelevskiy. Phase models and oscillators with time delayed coupling. Dynamics of Discrete and Continuous Systems. 32(8)(2012) 2653-2673. Reprint
  35. L. Zhang, S.A. Campbell and L. Huang. Nonlinear analysis of a maglev system with time-delayed feedback. Physica D 240(21) (2011) 1761-1770. Preprint
  36. R. Jessop and S.A. Campbell. Approximating the stability region of a neural network with a general distribution of delays. Neural Networks 23(10) (2010) 1187-1201. Preprint
  37. J. Milton, P. Naik, C. Chan and S.A. Campbell. Indecision in neural decision making models. Mathematical Modelling of Natural Phenomena. 5(2) (2010) 125-145.
  38. J. Milton, J.L. Cabrera, T. Ohira, S. Tajima, Y. Tonosaki and S.A. Campbell. The time-delayed inverted pendulum: Implications for human balance control. CHAOS 19 (2009) 026109. Preprint
  39. S.A. Campbell and R. Jessop. Approximating the stability region for a differential equation with a distributed delay. Mathematical Modelling of Natural Phenomena 4(2) (2009) 1-27. Preprint
  40. S.A. Campbell, E. Stone and T. Erneux. Delay induced canards in high speed machining. Dynamical Systems 24(3) (2009) 373-392. Preprint
  41. S.A. Campbell and Y. Yuan. Zero singularities of codimension two and three in delay differential equations. Nonlinearity 21(11) (2008) 2671-2691. Preprint
  42. S.A. Campbell, S. Crawford, K. Morris. Friction and the inverted pendulum stabilization problem. ASME J. Dynamic Systems, Measurement and Control 130(5) (2008) 054501. Preprint
  43. S. Kim, S.A. Campbell and X.Z. Liu. Delay independent stability of linear switching systems with time delay. J. Mathematical Analysis and Applications 339(2) (2008) 785-801. Preprint
  44. R. Taylor and S.A. Campbell. Approximating chaotic saddles for delay differential equations. Physical Review E 75(4) (2007) 046215.
  45. S. Bungay and S.A. Campbell. Patterns of oscillation in a ring of identical cells with delayed coupling. Int. J. Bifurcation and Chaos, 17(9) (2007), 3109 - 3125. DOI: 10.1142/S0218127407018907 Preprint.
  46. S.A. Campbell and E. Stone. Analysis of the chatter instability in a nonlinear model for drilling. ASME J. Computational and Nonlinear Dynamics 1(4) (2006), 294-306. Reprint.
  47. S.A. Campbell, I. Ncube and J. Wu. Multistability and stable asynchronous periodic oscillations in a multiple-delayed neural system. Physica D 214(2) (2006), 101-119.
  48. S. Kim, S.A. Campbell and X.Z. Liu. Stability of a class of linear switching systems with time delay. IEEE Transactions on Circuits and Systems I , 53(2) (2006), 384-393.
  49. S.A. Campbell, Y. Yuan and S. Bungay. Equivariant Hopf bifurcation in a ring of identical cells with delayed coupling. Nonlinearity, 18 (2005) 2827-2846. Reprint
  50. F.K. Skinner, H. Bazzazi and S.A. Campbell. Two-cell to N-cell heterogeneous, inhibitory networks: precise linking of multistable and coherent properties. J. Computational Neuroscience 18(3) (2005), 343-352. Reprint
  51. F.K. Skinner, J.Y.J. Chung, I. Ncube, P.A. Murray and S.A. Campbell. Using heterogeneity to predict inhibitory model characteristics. J. Neurophysiology 93 (2005), 1898-1907. Preprint
  52. M. Landry, S.A. Campbell, K. Morris and C.O. Aguilar Dynamics of an inverted pendulum with delayed feedback control. S.I.A.M. Journal on Applied Dynamical Systems 4(2) (2005) 333-351. Reprint Videos.
  53. S.A. Campbell, R. Edwards and P. van den Driessche. Delayed coupling between two neural network loops. S.I.A.M. Journal on Applied Mathematics 65(1) (2004), 316-335. https://doi.org/10.1137/S0036139903434833 Reprint
  54. E. Stone and S.A. Campbell. Stability and bifurcation analysis of a nonlinear DDE model for drilling. J. Nonlinear Science 14(1) (2004), 27-57. Reprint
  55. Y. Yuan and S.A. Campbell. Stability and synchronization in a ring of identical cells with delayed coupling. J. Dynamics and Differential Equations 16(3) (2004), 709-744. Special Issue in honour of the 60th birthday of Shui-Nee Chow. Reprint
  56. I. Ncube, S.A. Campbell and E.R. Vrscay. Stationary densities and the stochastic approximation of a certain class of random algorithms. Differential Equations and Dynamical Systems 11(1-2) (2003), 171-207.
  57. I. Ncube, S.A. Campbell and E.R. Vrscay. Stochastic approximation of a simple neural network-type learning algorithm via computer simulation. Dynamics of Continous, Discrete and Impulsive Systems Series B 10(2) (2003) 195-206.
  58. H. Zhu, S.A. Campbell and G.S.K. Wolkowicz. Bifurcation Analysis of a Predator-Prey System With Nonmonotonic Functional Response. SIAM J. Applied Mathematics 63(2) (2002), 636-682. Reprint
  59. S.A. Campbell. Delay Independent Stability for Additive Neural Networks. New millennium special issue on neural networks and neurocomputing -- theory, models, and applications, Part I. Differential Equations and Dynamical Systems 9(3-4) (2001), 115-138. Preprint
  60. S.A. Campbell and M. Waite, Multistability in Coupled Fitzhugh-Nagumo Oscillators. Nonlinear Analysis 47 (2001), 1093-1104.
  61. L.P. Shayer and S.A. Campbell, Stability, bifurcation and multistability in a system of two coupled neurons with multiple time delays. SIAM J. Applied Mathematics 61(2) (2000), 673-700. Reprint
  62. S.A. Campbell and Jacques Bélair, Resonant codimension two bifurcation in the harmonic oscillator with delayed forcing. Canadian Applied Mathematics Quarterly 7(3) (1999), 218-238. Reprint
  63. S.A. Campbell, S. Ruan and J. Wei, Qualitative analysis of a neural network model with multiple time delays. International J. Bifurcation and Chaos 9(8) (1999), 1585-1595.
  64. S.A. Campbell, Stability and bifurcation in the harmonic oscillator with multiple, delayed feedback loops. Dynamics of Continuous, Discrete and Impulsive Systems 5 (1999), 225-235.
  65. S.A. Campbell and V.G. LeBlanc, Resonant Hopf-Hopf interactions in delay differential equations. J. Dynamics and Differential Equations 10(2) (1998), 327-346. Reprint
  66. S.A. Campbell, Resonant codimension two bifurcation in a neutral functional differential equation, Nonlinear Analysis, Proceedings of the 1996 World Congress of Nonlinear Analysts, Vol. 30:7, (1997), 4577-4584.
  67. J. Bélair, S.A. Campbell and P. van den Driessche, Frustration, stability and delay-induced oscillations in a neural network model., SIAM Journal on Applied Mathematics 56(1), February (1996), 245-255. Reprint
  68. S.A. Campbell, J. Bélair, T. Ohira and J. Milton, Complex dynamics and multistability in a damped harmonic oscillator with delayed negative feedback. CHAOS 5(4) (1995), 1-6.
  69. S.A. Campbell and J. Bélair, Analytical and symbolically-assisted investigation of Hopf bifurcation in delay-differential equations. Canadian Applied Mathematics Quarterly 3(2) (1995), 137-154.
  70. S.A. Campbell, J. Bélair, T. Ohira and J. Milton, Limit cycles, tori and complex dynamics in a second-order differential equation with delayed negative feedback J. Dynamics and Differential Equations 7 (1995), 213-236. Reprint
  71. J. Milton, S.A. Campbell and J. Bélair, Dynamic feedback and the design of closed-loop drug delivery systems. J. Biological Systems 3 (1995), 711-718. Preprint
  72. J. Bélair and S.A. Campbell, Stability and bifurcations of equilibria in a multiple-delayed differential equation., S.I.A.M. Journal on Applied Mathematics 54(5), October (1994), 1402-1424. Reprint
  73. S.A. Campbell and P.J. Holmes, Heteroclinic cycles and modulated travelling waves in a system with D_4 symmetry., Physica D 59 (1992), 52-78.
  74. S.A. Campbell and P.J. Holmes, Bifurcation from O(2) symmetric heteroclinic cycles with three interacting modes., Nonlinearity 4 (1991), 697-726.

Book Chapters
  1. J. Milton, J. Wu, S.A. Campbell and J. Bélair Outgrowing neurological diseases: Microcircuits, conduction delay and childhood absence epilepsy. In: Computational Neurology and Psychiatry , P. Érdi, B. Sen Bhattacharya and A.L. Cochran, Eds. Springer, New York, 2017. DOI: 10.1007/978-3-319-49959-8_2. Preprint.
  2. J. Wu, S.A. Campbell and J. Bélair. Time-delayed neural networks: stability and oscillations. In Encyclopedia of Computational Neuroscience, D. Jaeger and R. Jung, editors. Springer, New York, 2018. (First appeared 2015)
  3. S.A. Campbell. Calculating centre manifolds for delay differential equations using Maple. In Delay Differential Equations: Recent Advances and New Directions , B. Balachandran, T. Kalmár-Nagy and D. Gilsinn, editors. Springer-Verlag, New York, 2009.
  4. S.A. Campbell. Time delays in neural systems. In Handbook of Brain Connectivity, R. McIntosh and V.K. Jirsa, editors. Springer-Verlag, 2007.
Conference Proceedings
  1. M.A. Chugunova, S.A. Campbell and M. Harris. (2025) Near-soma Activated Action Potential in Gonadotropin-releasing Hormone Neurons. In: Kilgour, D.M., Kunze, H., Makarov, R.N., Melnik, R., Wang, X. (eds) Addressing Modern Challenges in the Mathematical, Statistical, and Computational Sciences. AMMCS 2023. pp.295-304.
  2. K.-F. Hsueh, I. Al-Darabsah, M. Al Janaideh, S.A. Campbell and D. Kundur. Vulnerability of Connected Autonomous Vehicles Networks to Periodic Time-Varying Communication Delays of Certain Frequency. 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems , pp. 3452-3457. Prague, Czech Republic.
  3. I. Al-Darabsah, M. Al Janaideh, S.A. Campbell. Stability of Connected Autonomous Vehicle Networks with Commensurate Time Delays. 2021 American Control Conference, pp. 3308-3313. New Orleans, LA USA.
  4. I. Al-Darabsah, M. Al Janaideh, S.A. Campbell. The Effect of Input Signals Time-Delay on Stabilizing Traffic with Autonomous Vehicles. 2021 IEEE International Conference on Robotics and Automation, pp. 12708-12714. Xi'an, China,
  5. M. Ahmed and S.A. Campbell. Effect of genetic defects in a cortical circuit model associated with childhood absence epilepsy. In Recent Developments in Mathematical and Statistical and Computational Sciences, R.M. Kilgour, H. Kunze, R. Makarov, R. Melnik and S. Wang, Eds., pp. 477-487, Springer, 2020.
  6. J. Miller, H. Ryu, Z. Teymuroglu, X. Wang, V. Booth and S.A. Campbell. Clustering in inhibitory neural networks with nearest neighbor coupling. In Applications of Dynamical Systems in Biology and Medicine, T. Jackson and A. Radunskaya, Eds., pp. 99-121, Springer, New York, 2015. Preprint.
  7. Z. Wang and S.A. Campbell. Phase models and clustering in networks of oscillators with delayed, all-to-all coupling. Proceedings of the 12th IFAC Workshop on Time Delay Systems June 28-30, 2015, Ann Arbor MI, USA. Preprint.
  8. W. Nicola, F. Njap, K. Ferguson, F. Skinner and S.A. Campbell Mean field analysis gives accurate predictions of the behaviour of large networks of sparsely coupled and heterogeneous neurons. BMC Neuroscience 15 (Suppl 1) (2014) O3
  9. K. Ferguson and S.A. Campbell A two compartment model of a CA1 pyramidal neuron. Canadian Applied Mathematics Quarterly 17(2) (2009) 293-307, Special Issue for the 30th Anniversary of CAIMS. Reprint
  10. S. Bungay and S.A. Campbell Modelling a respiratory central pattern generator neuron in Lymnaea stagnalis. Canadian Applied Mathematics Quarterly 17(2) (2009) 283-291. Special Issue for the 30th Anniversary of CAIMS. Reprint
  11. S.A. Campbell, S. Crawford and K. Morris, Time delay and feedback control of an inverted pendulum with stick slip friction. Proceedings of the ASME 2007 International Design Engineering Technical Conferences.
  12. I. Ncube, S.A. Campbell and J. Wu, Change in criticality of synchronous Hopf bifurcation in a multiple-delayed neural system. In Dynamical Systems and Their Applications in Biology, S. Ruan, G.S.K. Wolkowicz and J. Wu eds. Fields Institute Communications 36, (2003), 179-193.
  13. K. Tchizawa and S.A. Campbell, On winding duck solutions in R4. Proceedings of the Second International Conference on Neural, Parallel and Scientific Computation Vol. 2 (2002) 315--318.
  14. S.A. Campbell, Stability and bifurcation of a simple neural network with multiple time delays. In Differential Equations with Application to Biology, G. Wolkowicz, S. Ruan and J. Wu eds. Fields Institute Communications 21, (1999), 65-79.
  15. S.A. Campbell and J. Bélair, Delays and tori in a nonlinear model from motor control. In Chaos in Biology and Medicine, W. Ditto., ed., Society of Photo-Optical Instrumentation Engineers (SPIE) Proceedings Series, vol. 2036, (1993), 256-268.
  16. S.A. Campbell and J. Bélair, Multiply delayed differential equations as models for physiological control systems. In World Congress of Nonlinear Analysts '92 , V. Lakshmikantham, ed., Walter de Gruyter, N.Y., 1996.

General Interest
  1. W. Nicola and S.A. Campbell. Nonsmooth Dynamical Systems in Neuroscience SIAM News June 2017.

This page maintained by Sue Ann Campbell.