Complex Biological Systems Group

Department of Mathematics, University of Pittsburgh


About Us






Theme Days 2012
Theme Days 2011
Theme Days 2010
Theme Days 2009

Complex Biological Systems Group
University of Pittsburgh
Department of Mathematics
301 Thackeray Hall
Pittsburgh, PA 15260
Tel: (412) 624-6157
Fax: (412) 624-8397



  • J.J. Rubin, J.E. Rubin & G.B. Ermentrout Analysis of synchronization in a slowly changing environment: how slow coupling becomes weak coupling, Phys. Rev. Lett., 110(20): 204101 (2013).
  • Rosenbaum, R., Rubin, J. E., & Doiron, B. Short-term synaptic depression and stochastic vesicle dynamics reduce and shape neuronal correlations, J. Neurophysiol., 109(2): 475-484 (2013).
  • Reich, S. & Rosenbaum, R., The impact of short term synaptic depression and stochastic vesicle dynamics on neuronal variability, J. Comp. Neurosci., accepted (2013).


  • C.J. Miller, G.B. Ermentrout & L.A. Davidson, Rotational model for actin filament alignment by myosin, J. Theor. Biol., 300:344-359 (2012).
  • K. Penner, B. Ermentrout & D. Swigon, Pattern formation in a model of acute inflammation, SIAM J. Appl. Dyn. Syst., 11: 629-660 (2012).
  • J. Arciero, G.B. Ermentrout, R. Siggers, A. Afrazi, D. Hackam, Y. Vodovotz, & J. Rubin, Modeling the interactions of bacteria and inflammation in necrotizing enterocolitis, J. Theor. Biol., accepted (2012).
  • S. Jayasuriya & Z.P. Kilpatrick, Effects of Time-Dependent Stimuli in a Competitive Neural Network Model of Perceptual Rivalry, Bull. Math. Biol., accepted (2012).
  • S.E. Folias & G.B. Ermentrout, Bifurcations of Stationary Solutions in an Interacting Pair of E–I Neural Fields, SIAM J. Appl. Dyn. Syst., accepted (2012).


  • S.E. Folias & G.B. Ermentrout, New Patterns of Activity in a Pair of Interacting Excitatory-Inhibitory Neural Fields, Phys. Rev. Lett., 107:228103 (2011).
  • S.E. Folias, Nonlinear Analysis of Breathing Pulses in a Synaptically Coupled Neural Network, SIAM J. Appl. Dyn. Syst., 10 (2011) pp. 744–787.
  • J.C. Arciero, Q. Mi, M.F. Branca, D. Hackam, & D. Swigon, Continuum Model of Collective Cell Migration in Wound Healing and Colony Expansion, Biophys. J., 100 (2011) pp. 535-543.
  • J. R. Dunmyre, C. A. Del Negro, & J. E. Rubin, Interactions of the CAN and persistent sodium current within a model respiratory neuron yield dynamically distinct bursting regimes, J. Comput. Neurosci. (accepted)
  • J. R. Dunmyre, Qualitative validation of the reduction from two reciprocally coupled neurons to one self-coupled neuron in a respiratory network model, J. Biol. Phys. (accepted)
  • H.F. Parks, G.B. Ermentrout & J.E. Rubin, The dynamics of a forced coupled network of active elements, Physica D, (in press)


  • S.E. Folias & G.B. Ermentrout, Spatially localized synchronous oscillations in synaptically coupled neuronal networks: conductance–based models and discrete maps, SIAM J. Appl. Dyn. Syst., 9 (2010), pp 1019-1060.
  • J. R. Dunmyre & J. E. Rubin, Optimal Intrinsic Dynamics for Bursting in a Three-Cell Network, SIAM J. Appl. Dyn. Syst., 9 (2010), pp. 154-187.
  • S. Lim, Y. Kim, & D. Swigon, Dynamics of an electrostatically charged rod in fluid, Proc. Roy Soc. A, online publication doi: 10.1098/rspa.2010.0174, 2010.
  • Arciero, J.C., Ermentrout, G.B., Upperman, J.S., Vodovotz, Y., & Rubin, J.E. (2010) Using a Mathematical Model to Analyze the Role of Probiotics and Inflammation in Necrotizing Enterocolitis. PLoS ONE 5(4): e10066. doi:10.1371/journal.pone.0010066


  • T.L. Stepien. Tubuloglomerular Feedback-Mediated Dynamics in Three Coupled Nephrons. SIURO 2(1): 1-25, 2009.
  • B. Riviere, Y. Epshteyn, D. Swigon, & Y. Vodovotz, A Mathematical Model of Signaling Resulting from the Binding of Lipopolysaccharide with Toll-like Receptors Demonstrates Inherent Preconditioning Behavior, Math. Biosciences 217: 19-26, 2009.
  • S. Bayram, T.L. Stepien, E.B. Pitman. TGF-Mediated Dynamics in a System of Many Coupled Nephrons. Bull. Math. Biol. 71: 1482-1506, 2009.
  • J. Rubin, N. Shevtsova, B. Ermentrout, J. Smith, I. Rybak. Multiple rhythmic states in a model of the respiratory CPG. J. Neurophysiol. 101: 2146-2165, 2009.
  • J. Rubin, J. Hayes, J. Mendenhall, C. Del Negro. Calcium-activated nonspecific cation current and synaptic depression promote network-dependent burst oscillations. Proc. Natl. Acad. Sci. USA 106: 2939-2944, 2009
  • Ermentrout B, Ko TW, Delays and weakly coupled neuronal oscillators, Philosophical Transactions of the Royal Society A – Mathematical Physical and Engineeering Sciences, 367:1097-1115,2009
  • Ko TW, Ermentrout GB, Phase-response curves of coupled oscillators Phys Rev E:79: 016211, 2009
  • Y. Vodovotz, G. Constantine, J. Rubin, M. Csete, E. Voit, G. An, Mechanistic simulations of inflammation: Current state and future prospects, Math. Biosci., 217: 1-10, 2009


  • I. Aavatsmark, G.T. Eigestad, R.A. Klausen, M. F. Wheeler, and I. Yotov. Convergence of a symmetric mpfa method on quadrilateral grids. Computational Geosciences. (accepted)
  • Arciero, J.C., Carlson, B.E., Secomb, T.W. Roles of oxygen-dependent ATP release by red blood cells and conducted responses in metabolic regulation of blood flow. Am J Physiol. Heart. Circ. Physiol. 295:H1562-H1571, 2008.
  • Carlson, B.E., Arciero, J.C., Secomb, T.W. Relative influence of myogenic, shear-dependent, and conducted responses on vascular autoregulation. Am. J. Physiol. Heart. Circ. 367:1097-1115 2009
  • Ko TW, Ermentrout GB, Bistability between synchrony and incoherence in limit-cycle oscillators with coupling strength inhomogeneity, Phys Rev E 78: 026210, 2008
  • S. Daun, J. Rubin, I. Rybak. Control of oscillation periods and phase durations in half-center central pattern generators: a comparative mechanistic analysis. J. Comp. Neurosci., accepted.
  • S. Daun, J. Rubin, Y. Vodovotz, A. Roy, R. Parker, G. Clermont. An ensemble of models of the acute inflammatory response: results from parameter reduction. J. Theor. Biol., 253:843-853, 2008.
  • G. B. Ermentrout, R.F. Galan, and N. N. Urban. Reliability, synchrony and noise. Trends in Neuroscience, 31:428-434, 2008.
  • R.F. Galan, G.B. Ermentrout, and N.N. Urban. Optimal time scale for spike-time reliability: Theory, simulations and experiments. J. of Neurophysiol., 99(1):277-283, 2008.
  • U. Girault, S. Sun, M. F. Wheeler, and I. Yotov. Coupling discontinuous galerkin and mixed finite element discretizations using mortar finite elements. Submitted to SIAM J. Numer. Anal.
  • Y. Guo, J. Rubin, C. McIntyre, J. Vitek, and D. Terman. Thalamocortical relay fidelity varies across subthalamic nucleus deep brain stimulation protocols in a data-driven computational model. J. Neurophysiol., 99:1477-1492, 2008.
  • F.G. Kazanci, and G.B. Ermentrout. Wave formation through the interactions between clustered states and local coupling in arrays of neural oscillators. SIAM J. Appl. Dyn. Syst., 7(2):491-509, 2008.
  • T.W. Ko, and G.B. Ermentrout. Partially locked states in coupled oscillators due to inhomogeneous coupling. Physical Review E, 78(1):016203, 2008.
  • T.W. Ko, and G.B. Ermentrout. Bistability between synchrony and incoherence in limit-cycle oscillators with coupling strength inhomogeneity. Physical Review E, 78;026210, 2008.
  • N. Li, K. Verdolini, G. Clermont, Q. Mi, P. Hebda, and Y. Vodovotz. A patient-specific in silico model of inflammation and healing tested in acute vocal fold injury. Submitted.
  • K. Lipnikov, M. Shashkov, and I. Yotov. Local flux mimetic finite difference methods. Submitted to Numer. Math.
  • S. Marella, and G.B. Ermentrout. Class-II neurons display a higher degree of stochastic synchronization than class-I neurons. Physical Review E, 77(4):041918, 2008.
  • Q. Mi, B. Riviere, G. Clermont, D.L. Steed, and Y. Vodovotz. Agent-based modeling of inflammation and wound healing: insights into diabetic foot ulcer pathology and the role of transforming growth factor-beta 1. Wound Repair and Regeneration, To appear.
  • A. Reynolds, G. Clermont, J. Rubin, et al. A mathematical model of acute inflammation which accounts for blood and tissue ineractions. Shock, 22:84-85, 2008.
  • J. Rubin, M. Wechselberger. The selection of mixed mode oscillations in a Hodgkin-Huxley model with multiple timescales. Chaos, 18:015105-1--015105-12, 2008.