Stochastic and nonequilibrium processes
Stochastic models of intracellular transport
Neural field theory and vision
P. C. Bressloff. Kuramoto model with stochastic resetting and coupling through an external medium. Chaos 35 023162 (2025)
P. C. Bressloff. A generalized Dean-Kawasaki equation for an interacting Brownian gas in a partially absorbing medium. Proc.Roy. Soc. A 480 20230915 (2024)
P. C. Bressloff. Global density equations for interacting particle systems with stochastic resetting: From overdamped Brownian motion to phase synchronization. Chaos 34 043101 (2024)
P. C. Bressloff. Global density equations for a population of actively switching particles. J. Phys. A 57 085001 (2024)
P. C. Bressloff. Generalized Ito’s lemma and the stochastic thermodynamics of diffusion with resetting. J. Phys. A. 57 445003 (2024)
P. C. Bressloff. Transition path theory for diffusive search with stochastic resetting. J. Phys. A 57 145001 (2024)
P. C. Bressloff. Truncated stochastically switching processes. Phys. Rev. E 109 024103 (2024)
P. C. Bressloff. Accumulation time of stochastic processes with resetting. J. Phys. A 54 354001 (2021)
R. D. Schumm and P. C. Bressloff. Search processes with stochastic resetting and partially absorbing targets. J. Phys. A 54 404004 (2021)
P. C. Bressloff. Drift-diffusion on a Cayley tree with stochastic resetting: the localization-delocalization transition. J. Stat. Mech. 063206 (2021)
P. C. Bressloff. Stochastic resetting and the mean-field dynamics of focal adhesions. Phys. Rev. E 102 022134 (2020)
P. C. Bressloff. Switching diffusions and stochastic resetting. J. Phys. A 53 275003 (2020)
P. C. Bressloff. Diffusive search for a stochastically-gated target with resetting. J. Phys. A 53 425001 (2020)
P. C. Bressloff. Queueing theory of search processes with stochastic resetting. Phys. Rev. E 102 032109 (2020)
P. C. Bressloff. Search processes with stochastic resetting and multiple targets. Phys. Rev. E 102 022115 (2020)
P. C. Bressloff. Modeling active cellular transport as a directed search process with stochastic resetting and delays. J. Phys. A 53 355001 (2020)
P. C. Bressloff. Directed intermittent search with stochastic resetting. J. Phys. A 53 105001 (2020)
P. C. Bressloff. Entropy production for diffusion processes across a semipermeable interface. Phys. Rev. Res. 6 023283 (2024).
R. D. Schumm and P. C. Bressloff. A numerical method for solving snapping out Brownian motion in 2D bounded domains. Journal of Computational Physics 493 (2023).
P. C. Bressloff. Renewal equations for single-particle diffusion in multi-layered media. SIAM Journal on Applied Mathematics 83 1518-1545 (2023).
P. C. Bressloff. Diffusion with stochastic resetting screened by a semi-permeable interface. J. Phys. A 56 105001 (2023).
P. C. Bressloff. Renewal equations for single-particle diffusion through a semi-permeable interface. Phys. Rev. E 107 014110(2023).
P. C. Bressloff. A probabilistic model of diffusion through a semi-permeable barrier. Proc. Roy. Soc. A 478 2022.0615 (2022).
P. C. Bressloff. Encounter-based reaction-subdiffusion model II: partially absorbing traps and the occupation time propagator. J. Phys. A 56 435005(2023).
P. C. Bressloff. Encounter-based reaction-subdiffusion model I: surface adsorption and the local time propagator. J. Phys. A 56 435004 (2023).
P. C. Bressloff. Close encounters of the sticky kind: Brownian motion at absorbing boundaries. Physical Review E 107 064121 (2023).
P. C. Bressloff. Stochastically switching diffusion with partially reactive surfaces. Phys. Rev. E 106 034108 (2022).
P. C. Bressloff. Accumulation times for diffusion-mediated surface reactions. J. Phys. A 55 415002 (2022).
P. C. Bressloff. Spectral theory of diffusion in partially absorbing media. Proc. Roy. Soc A 478 20220319 (2022).
P. C. Bressloff. Diffusion in a partially absorbing medium with position and occupation time resetting. J. Stat. Mech. 063207 (2022).
P. C. Bressloff. Diffusion-mediated surface reactions and stochastic resetting. J. Phys. A 55 275002 (2022).
P. C. Bressloff. Diffusion-mediated absorption by partially reactive targets: Brownian functionals and generalized propagators. J. Phys. A 55 205001 (2022).
P. C. Bressloff. Asymptotic analysis of particle cluster formation in the presence of anchoring sites. Eur. J. Phys. E 47 30 (2024)
P. C. Bressloff. Asymptotic analysis of conversion-limited phase separation. Proc. Roy. Soc. A 480 2023.0725 (2024)
P. C. Bressloff. Two-dimensional Ostwald ripening in a concentration gradient. J. Phys. A 53 365002 (2020)
P. C. Bressloff. Active suppression of Ostwald ripening: Beyond mean field theory. Phys. Rev. E 101 042804 (2020)
P. C. Bressloff. Cellular diffusion processes in singularly perturbed domains. J. Math. Biology. 89 58 (2024).
P. C. Bressloff. The 3D narrow capture problem for traps with semipermeable interfaces. Multiscale Modeling & Simulation 21 (2023).
P. C. Bressloff. The narrow capture problem: an encounter-based approach to partially reactive targets. Phys. Rev. E 105 034141 (2022)
P. C. Bressloff. Accumulation time of diffusion in a 3D singularly perturbed domain. SIAM J. Appl. Math. 83 862-881 (2023)
P. C. Bressloff. Accumulation time of diffusion in a 2D singularly perturbed domain. Proc. Roy. Soc A 478 20210847 (2022)
P. C. Bressloff and R. D. Schumm. The narrow capture problem with partially absorbing targets and stochastic resetting. Multiscale Model. Simul. 20 857-881 (2022)
P. C. Bressloff. Asymptotic analysis of target fluxes in the three-dimensional narrow capture problem. Multiscale Model. Simul. 19 612-632 (2021)
P. C. Bressloff. Asymptotic analysis of extended two-dimensional narrow capture problems. Proc Roy. Soc. A 477 20200771 (2021)
P. C. Bressloff. Trapping of an active Brownian particle at a partially absorbing wall. Proc. Roy. Soc. A 479 2023.0086 (2023).
P. C. Bressloff. Encounter-based model of a run-and-tumble particle II: absorption at sticky boundaries. J. Stat. Mech. 043208 (2023).
P. C. Bressloff. Encounter-based model of a run-and-tumble particle. J. Stat. mech. 113206 (2022).
P. C. Bressloff. Occupation time of a run-and-tumble particle with resetting. Phys. Rev. E 102 042135 (2020)
P. C. Bressloff and S. D. Lawley. Hybrid colored noise process with space-dependent switching rates. Phys. Rev. E 96 012129 (2017).
P. C. Bressloff and S. D. Lawley. Temporal disorder as a mechanism for spatially heterogeneous diffusion. Phys. Rev. E 95 060101(R) (2017).
P. C. Bressloff and S. D. Lawley. Residence times of a Brownian particle with temporal heterogeneity. J. Phys. A 50 195001 (2017).
P. C. Bressloff. Stochastically-gated local and occupation times of a Brownian particle. Phys. Rev. E 95 012130 (2017).
P. C. Bressloff. Stochastic Fokker-Planck equation in random environments. Phys. Rev. E 94 042129 (2016).
P. C. Bressloff and S. D. Lawley. Escape from subcellular domains with randomly switching boundaries. Multiscale Model. Simul. 13 1420-1445 (2015).
P. C. Bressloff and S. D. Lawley. Stochastically-gated diffusion-limited reactions for a small target in a bounded domain. Phys. Rev. E 92 062117 (2015).
P. C. Bressloff and S. D. Lawley. Escape from a potential well with a switching boundary. J. Phys. A 48 225001 (2015).
P. C. Bressloff and S. D. Lawley. Moment equations for a piecewise deterministic PDE. J. Phys. A 48 105001 (2015).
P. C. Bressloff and J. M. Newby. Stochastic models of intracellular transport (Review) Rev. Mod. Phys. 85 135-196 (2013).
P. C. Bressloff. Directional search-and-capture model of cytoneme-based morphogenesis. SIAM J. Appl. Math 81 919-938 (2021)
P. C. Bressloff and H. Kim. A search-and-capture model of cytoneme-mediated morphogen gradient formation Phys. Rev. E 99 052401 (2019).
H. Kim and P. C. Bressloff. Impulsive signaling model of cytoneme-based morphogen gradient formation Phys. Biol. 16 056005 (2019).
H. Kim and P. C. Bressloff. Direct vs. synaptic contacts in a mathematical model of cytoneme-based morphogen gradient formation SIAM J. Appl. Math 78 2323-2347 (2018).
P. C. Bressloff and H. Kim. Bidirectional transport model of morphogen gradient formation via cytonemes Phys. Biol. 15 026010 (2018).
P. C. Bressloff. Morphogen gradient formation in partially absorbing media. Phys. Biol. 19 066005 (2022).
P. Murphy, P. C. Bressloff and S. D. Lawley. Interaction between switching diffusivities and cellular microstructure. Multiscale Model. Simul. 18 572-588 (2020)
P. C. Bressloff, S. D. Lawley and P. Murphy. Protein concentration gradients and switching diffusions Phys. Rev. E 99 032409 (2019)
P. C. Bressloff. Local accumulation time for diffusion in cells with gap junction coupling. Phys. Rev. E 105 034404 (2022)
P. C. Bressloff. Local accumulation time for diffusion in cells with gap junction coupling. Phys. Rev. E 105 034404 (2022).
P. C. Bressloff. Stochastically-gated diffusion model of selective nuclear transport. Phys. Rev. E 101 042404 (2020)
P. Murphy, P. C. Bressloff and S. D. Lawley. Interaction between switching diffusivities and cellular microstructure. Multiscale Model. Simul. 18 572-588 (2020)
P. C. Bressloff, S. D. Lawley and P. Murphy. Effective permeability of gap junctions with age-structured switching SIAM J. Appl. Math 80 312-337 (2020)
P. C. Bressloff, S. D. Lawley and P. Murphy. Diffusion in an age-structured randomly switching environment J. Phys. A 51 315001 (2018).
P. C. Bressloff and S. D. Lawley. Dynamically active compartments coupled by a stochastically-gated gap junction. J. Nonlin. Sci. 27 1487–1512 (2017)
P. C. Bressloff and S. D. Lawley. Diffusion on a tree with stochastically-gated nodes. J. Phys. A 49 245601 (2016).
P. C. Bressloff. Diffusion in cells with stochastically-gated gap junctions. SIAM J. Appl. Math. 76 1658-1682 (2016).
P. C. Bressloff. 2D interfacial diffusion model of inhibitory synaptic receptor dynamics. Proc. Roy. Soc. A 479 2022.0831 (2023).
R. D. Schumm and P. C. Bressloff. Local accumulation times in a diffusion-trapping model of synaptic receptor dynamics. Phys. Rev. E 105 064407 (2022).
P. C. Bressloff}. Propagation of CaMKII translocation waves in heterogeneous spiny dendrites. J. Math. Biol. 66 1499-1525 (2013).V. M. Burlakov, N.Emptage, A. Goriely and P. C. Bressloff. Synaptic bistability due to nucleation and evaporation of receptor clusters. Phys. Rev. Lett. 108 028101 (2012)
B. A. Earnshaw and P. C. Bressloff. Diffusion-activation model for CaMKII translocation waves in dendrites. J. Comp. Neurosci. 28 77-89 (2010).
P. C. Bressloff. Cable theory of protein receptor trafficking in dendritic trees. Phys. Rev. E 79 041904 (2009).
P. C. Bressloff and B. A. Earnshaw. A dynamical corral model of protein trafficking in spines. Biophys. J. 96 1786-1802 (2009).
P. C. Bressloff, B. A. Earnshaw and M. J. Ward. Diffusion of protein receptors on a cylindrical dendritic membrane with partially absorbing traps. SIAM J. Appl. Math. 68 1223-1246 (2008).
B. A. Earnshaw and P. C. Bressloff, A biophysical model of AMPA receptor trafficking and its regulation during LTP/LTD. J. Neurosci. 26 12362-12373 (2006).
P. C. Bressloff. A stochastic model of protein receptor trafficking prior to synaptogenesis. Phys. Rev. E 74 031910 (2006).
P. C. Bressloff. Queuing model of axonal transport. Brain Multiphysics 2 100042 (2021)
B. Karamched and P. C. Bressloff. Effects of geometry on reversible vesicular transport. J. Phys. A 50 055601 (2017).
P. C. Bressloff and B. Karamched. Model of reversible vesicular transport with exclusion J. Phys. A 49 345602 (2016).
P. C. Bressloff. Aggregation-fragmentation model of vesicular transport in neurons. J. Phys. A 49 145601 (2016).
P. C. Bressloff and E. Levien. Synaptic democracy and active intracellular transport in axons. Phys. Rev. Lett. 114 168101 (2015).
P. C. Bressloff. Two-pool model of cooperative vesicular transport. Phys. Rev. E 86 031911 (2012).
P. C. Bressloff and J. Newby. Quasi-steady state analysis of motor-driven transport on a two-dimensional microtubular network. Phys. Rev. E 83 061139 (2011).
J. Newby and P. C. Bressloff. Local synaptic signalling enhances the stochastic transport of motor-driven cargo in neurons. Phys. Biol. 7 036004 (2010).
J. Newby and P. C. Bressloff. Random intermittent search and the tug-of-war model of motor-driven transport. J. Stat. Mech. P04014 (2010).
J. Newby and P. C. Bressloff. Quasi-steady state reduction of molecular-based models of directed intermittent search. Bull. Math. Biol. 72 1840-1866 (2010).
J. Newby and P. C. Bressloff. Directed intermittent search for a hidden target on a dendritic tree network. Phys. Rev. E 021913 (2009).
P. C. Bressloff and J. Newby. Intermittent search strategies for delivering mRNA particles to synaptic targets. New J. Phys. 11 023033 (2009).
P. C. Bressloff. Multi-spike solutions of a hybrid reaction-transport model. Proc Roy. Soc. A 477 20200829 (2021)
H. Kim and P. C. Bressloff. Stochastic Turing pattern formation in a model with active and passive transport. Bull. Math. Biol. 82 144 (2020)
H. A. Brooks and P. C. Bressloff. Turing mechanism for homeostatic control of synaptic density in C. elegans. Phys. Rev. E 96 012413 (2017).
H. A. Brooks and P. C. Bressloff. A mechanism for Turing pattern formation with active and passive transport. SIAM J. Appl. Dyn. Syst. 15 1823-1843 (2016).
P. C. Bressloff and B. Karamched. A doubly stochastic Poisson model of flagellar length control. SIAM J. Appl. Math 78 719-741 (2018).
P. C. Bressloff and B. Karamched. A frequency-dependent decoding mechanism for axonal length sensing. Front. Cellular Neurosci. 9 281 (2015).
B. Karamched and P. C. Bressloff. A delayed feedback model of axonal length sensing. Biophys. J 108 2408-2419 (2015).
P. C. Bressloff. A stochastic model of intraflagellar transport. Phys. Rev. E 73 061916 (2006).
Bin Xu and P. C. Bressloff. A theory of synchrony for active compartments with delays coupled through bulk diffusion Physica D 341 45-59 (2017).
Bin Xu and P. C. Bressloff. A PDE-DDE model for cell polarization in fission yeast SIAM J. Appl. Math 76 1844-1870 (2016).
Bin Xu and P. C. Bressloff. Model of growth cone membrane polarization via microtubule length regulation. Biophys. J. 109 2203-2214 (2015).
P. C. Bressloff and B. Xu. Stochastic active-transport model of cell polarization. SIAM J. Appl. Appl. Math. 75 652-678 (2015).
P. C. Bressloff. Stochastic switching in biology: from genotype to phenotype (Invited topical review). J. Phys. A 50 055601 (2017).
P. C. Bressloff. Construction of stochastic hybrid path integrals using operator methods. J. Phys. A 54 185001 (2021)
P. C. Bressloff. Coherent spin states and stochastic hybrid path integrals. J. Stat. Mech. 043207 (2021)
P. C. Bressloff. Stochastic switching in biology: from genotype to phenotype (Invited topical review). J. Phys. A 50 055601 (2017).
P. C. Bressloff and O. Faugeras. On the Hamiltonian structure of large deviations in stochastic hybrid systems. J. Stat. Mech. 033206 (2017).
P. C. Bressloff and S. D. Lawley. Mean first passage times for piecewise deterministic Markov processes and the effects of critical points. J. Stat. Mech. 063202 (2017).
P. C. Bressloff. Feynman-Kac formula for stochastic hybrid systems. Phys. Rev. E 95 012138 (2017).
P. C. Bressloff. Path-integral methods for analyzing the effects of fluctuations in stochastic hybrid neural networks. J. Math. Neurosci 5 33pp. (2015).
P. C. Bressloff and J. M. Newby. Path-integrals and large deviations in stochastic hybrid systems. Phys. Rev. E 89 042701 (2014).
P. C. Bressloff and J. M. Newby. Stochastic hybrid model of spontaneous dendritic NMDA spikes. Phys. Biol. 11 016006 (13pp) (2014).
J. M. Newby, P. C. Bressloff and J. P. Keener. The effect of Potassium channels on spontaneous action potential initiation by stochastic ion channels. Phys. Rev. Lett. 111 128101 (2013).
P. C. Bressloff and J. M. Newby. Metastability in a stochastic neural network modeled as a jump velocity Markov process. SIAM J. Appl. Dyn. Syst. 12 1394-1435 (2013).
P. C. Bressloff. Metastable states and quasicycles in a stochastic Wilson-Cowan model of neural population dynamics. Phys. Rev. E. 82 051903 (2010).
P. C. Bressloff and J. Maclaurin. Phase Reduction of Stochastic CRN Oscillators. SIAM J. Appl. Dyn. Sys. 19 151-180 (2020).
P. C. Bressloff and J. Maclaurin. Synchronization of stochastic hybrid oscillators driven by a common switching environment Chaos 28 123123 (2018).
P. C. Bressloff and J. Maclaurin. A variational method for analyzing limit cycle oscillations in stochastic hybrid systems. Chaos 28 063105 (2018).
P. C. Bressloff and J. Maclaurin. A variational method for analyzing stochastic limit cycle oscillators SIAM J. Appl. Dyn. 17 2205-2233 (2018).
Y-M Lai, J. Newby and P. C. Bressloff. Effects of demographic noise on the synchronization of metacommunities by a fluctuating environment. Phys. Rev. Lett. 107 118102 (2011)
P. C. Bressloff and Y-M Lai. Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise. J. Math. Neurosci. 1 (2011)
E. Levien and P. C. Bressloff. Effects of a common noisy environment on correlations in downstream gene transcription. Bull Math Biol. 81 800-829 (2019).
E. Levien and P. C. Bressloff. Robustness of stochastic chemical reaction networks to extrinsic noise: the role of deficiency. Multiscale Model. Simul. 16 1519-1541 (2018).
E. Levien and P. C. Bressloff. Reversibility and stationary distributions in hybrid chemical reaction networks. J. Phys. A 50 475004 (2017).
E. Levien and P. C. Bressloff. Coupling sample paths to the thermodynamic limit in Monte Carlo estimators with applications to gene expression. J. Comp. Phys. 346 1-13 (2017).
G. Fan and P. C. Bressloff. Modeling the role of feedback in the adaptive response of bacterial quorum sensing. Bull. Math. Biol. 81 1479-1505 (2019).
G. Fan and P. C. Bressloff. Population model of quorum sensing with multiple pathways. Bull. Math. Biol. 79 2599-2626 (2017).
P. C. Bressloff. Ultrasensitivity and noise amplification in a model of V. harveyi quorum sensing. Phys. Rev. E 93 062418 (2016).
P. C. Bressloff. Spatiotemporal dynamics of continuum neural fields: Invited Topical review. J. Phys. A 45 033001 (2012).
P. C. Bressloff and S. R. Carroll. Stochastic neural fields as gradient dynamical systems. Phys. Rev. E 100 012402 (2019).
P. C. Bressloff. Stochastic neural field theory of wandering bumps on a sphere. Physica D 399 138-152 (2019).
P. C. Bressloff. Stochastic neural field model of stimulus-dependent neural variability. PLoS Comp. Biol. 15 e1006755 (2019).
P. C. Bressloff and Z. P. Kilpatrick. Nonlinear Langevin equations for the wandering of fronts in stochastic neural fields. SIAM J. Appl. Dyn. Syst. 14 305-334 (2015).
P. C. Bressloff. From invasion to extinction in heterogeneous neural fields. J. Math. Neurosci. 2 6 (2012).
P. C. Bressloff and M. A. Webber. Front Propagation in stochastic neural fields. SIAM J. Appl. Dyn. Syst. 11 708-740 (2012).
P. C. Bressloff. Stochastic neural field theory and the system-size expansion. SIAM J. Appl. Math. 70 1488--1521 (2009).
P. C. Bressloff and Z. Kilpatrick. Two-dimensional bumps in a piecewise smooth neural field model with synaptic depression. SIAM J. Appl. Math 71 379-408 (2011).
Z. Kilpatrick and P. C. Bressloff. Stability of bumps in piecewise smooth neural fields with nonlinear adaptation. Physica D 239 1048-1060 (2010).
Z. Kilpatrick and P. C. Bressloff. Effects of synaptic depression and adaptation on spatiotemporal dynamics of an excitatory neuronal network. Physica D 239 547-560 (2010).
Z. Kilpatrick and P. C. Bressloff. Spatially structured oscillations in a two--dimensional neuronal network with synaptic depression. J. Comp. Neurosci. 28 193-209 (2010).
Z. Kilpatrick, S. E. Folias and P. C. Bressloff. Traveling pulses and wave propagation failure in an inhomogeneous neural network. SIAM J. Appl. Dyn. Syst. 7 161-185 (2008).
P. C. Bressloff. Weakly interacting pulses in synaptically coupled excitable neural media. SIAM J. Appl. Math. 66 57-81 (2006).
S. E. Folias and P. C. Bressloff. Stimulus-locked traveling waves and breathers in an excitatory neural network. SIAM J. Appl. Math. 65 2067-2092 (2005).
S. E. Folias and P. C. Bressloff. Breathers in two-dimensional neural media. Phys. Rev. Lett. 95 208107 (2005).
P. C. Bressloff and S. E. Folias. Front bifurcations in an excitatory neural network SIAM J. Appl. Math. 65 131-151 (2005).
S. E. Folias and P. C. Bressloff. Breathing pulses in an excitatory neural network SIAM J. Dyn. Syst. 3 378-407 (2004).
P. C. Bressloff, S. Folias, A Prat and Y-X Li. Oscillatory waves in inhomogeneous neural media Phys. Rev. Lett. 91 178101 (2003).
P. C. Bressloff. Traveling fronts and wave propagation failure in an inhomogeneous neural network. Physica D 155 83-100 (2001).
S. Carroll and P. C. Bressloff. Binocular rivalry waves in directionally selective neural field models. Physica D 285 8-17 (2014).
M. A. Webber and P. C. Bressloff. The effects of noise on binocular rivalry waves: a stochastic neural field model. J. Stat. Mech. 3 P03001 (2013).
P. C. Bressloff and M. A. Webber. Neural field model of binocular rivalry waves. J. Comput. Neurosci. 32 233-252 (2012).
Z. P. Kilpatrick and P. C. Bressloff. Binocular rivalry in a competitive neural network with synaptic depression. SIAM J. Appl. Dyn. Syst. 9 1303-1347 (2010).
S. Carroll and P. C. Bressloff. Symmetric bifurcations in a neural field model for encoding the direction of spatial contrast gradients. SIAM J. Appl. Dyn. Syst. 17 1-51 (2018).
S. Carroll and P. C. Bressloff. Phase equation for patterns of orientation selectivity in a neural field model of visual cortex. SIAM J. Appl. Dan. Syst. 15 60-83 (2016).
P. C. Bressloff and S. Carroll. Laminar neural field model of laterally propagating waves of orientation selectivity. PLoS Comput. Biol. 11 e1004545 (2015).
P. C. Bressloff and S. M. Carroll. Spatio-temporal dynamics of neural fields on product spaces. SIAM J. Appl. Dyns. Syst. 13 1620-1653 (2014).
P. C. Bressloff and J. D. Cowan. A spherical model for orientation and spatial-frequency tuning in a cortical hypercolumn. Phil. Trans. Roy. Soc. Lond. B 357 1643-1667 (2003).
P. C. Bressloff and J. D. Cowan. An amplitude approach to contextual effects in primary visual cortex. Neural Comput. 14 493-525 (2002).
P. C. Bressloff. Spatially periodic modulation of cortical patterns by long-range horizontal connections. Physica D 185 131-157 (2003).
P. C. Bressloff and J. D. Cowan. Functional geometry of local and horizontal connections in a model of V1. J. Physiol. (Paris) 97 221-236 (2003).
P. C. Bressloff. Bloch waves, periodic feature maps and cortical pattern formation. Phys. Rev. Lett. 89 088101 (2002).
P. C. Bressloff and J. D. Cowan. The visual cortex as a crystal. Physica D 173 226-258 (2002).
P. C. Bressloff, J. D. Cowan, M. Golubitsky and P. J. Thomas. Scalar and pseudoscalar bifurcations: pattern formation on the visual cortex. Nonlinearity 14 739-775 (2001).
P. C. Bressloff, J. D. Cowan, M. Golubitsky, P. J. Thomas and M. Wiener. Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex. Phil. Trans. Roy. Soc. Lond. B 356 299-330 (2001).
A. M. Oster and P. C. Bressloff. A developmental model of ocular dominance formation on a growing cortex. Bull. Math Biol. 68 73-98 (2006).
P. C. Bressloff. Spontaneous symmetry breaking in self-organizing neural fields. Biol. Cybern. 93 256-274 (2005).
P. C. Bressloff and S. Coombes. Saltatory waves in the spike-diffuse-spike model of active dendritic spines. Phys. Rev. Lett. 91 028102 (2003).
S. Coombes and P. C. Bressloff. Solitary waves in a model of dendritic cable with active spines. SIAM J. Appl. Math. 61, 432-453 (2000).
P. C. Bressloff and S. Coombes. Dynamics of strongly coupled spiking neurons. Neural Comput. 12, 91-129 (2000).
P. C. Bressloff and S. Coombes. Dynamical theory of spike train dynamics in networks of integrate-and-fire oscillators. SIAM J. Appl. Math. 60, 820-841 (2000).
P. C. Bressloff and S. Coombes. Symmetry and phase-locking in a ring of pulse--coupled oscillators with distributed delays. Physica D 126, 99-122 (1999).
P. C. Bressloff. Traveling waves and pulses in a one-dimensional network of integrate-and-fire neurons. J. Math. Biol. 40, 169-198 (2000).
P. C. Bressloff, N. W. Bressloff and J. D. Cowan. Dynamical mechanism for sharp orientation tuning in an IF model of cortical hypercolumns. Neural Comput. 12, 2473-2511 (2000).
P. C. Bressloff. Resonant-like synchronization and bursting in a model of pulse-coupled neurons with active dendrites. J. Comput. Neurosci. 6, 237-249 (1999).
P. C. Bressloff and S. Coombes. Travelling waves in a chain of pulse-coupled integrate-and-fire oscillators with distributed delays. Physica D 130, 232-254 (1999).
P. C. Bressloff. Mean-field theory of globally coupled integrate-and-fire neural oscillators with dynamic synapses. Phys. Rev. E 60, 2180-2190 (1999).
S. Coombes and P. C. Bressloff. Mode-locking and Arnold tongues in integrate-and-fire neural oscillators. Phys. Rev. E 60, 2086-2096 (1999).
P. C. Bressloff. Synaptically generated wave propagation in excitable neural media. hys. Rev. Lett. 82, 2979-2982 (1999).
P. C. Bressloff and S. Coombes. Spike-train dynamics underlying pattern formation in integrate-and-fire oscillator networks. Phys. Rev. Lett. 81, 2384-2387 (1998).
P. C. Bressloff and S. Coombes. Desynchronization, mode-locking and bursting in coupled integrate-and-fire oscillators. Phys. Rev. Lett. 81, 2168-2171 (1998).
P. C. Bressloff and S. Coombes. Traveling waves in chain of pulse-coupled oscillators. Phys. Rev. Lett. 80, 4815-4818 (1998).
P. C. Bressloff, S. Coombes and B. De Souza. Dynamics of a ring of pulse-coupled oscillators: Group theoretic approach. Phys. Rev. Lett. 79, 2791-2794 (1997).
P. C. Bressloff and S. Coombes. Synchrony in an array of integrate-and-fire neurons with dendritic structure. Phys. Rev. Lett. 78, 4665-4668 (1997).
P. C. Bressloff and S. Coombes. Physics of the extended neuron. Int. J. Mod. Phys. B 11, 2343-2392 (1997).
P. C. Bressloff and C. V. Wood. Spontaneous oscillations in a nonlinear delayed feedback shunting model of the pupil light reflex. Phys. Rev. E 58, 3597-3606 (1998).
P. C. Bressloff, C. V. Wood and P. A. Howarth. Nonlinear shunting model of the pupil light reflex. Proc. Roy. Soc. B 263, 953-960 (1996).
P. C. Bressloff. A Self-organizing network in the weak coupling limit. Physica D 110, 195-208 (1997).
P. C. Bressloff and G. Rowlands. Exact travelling wave solutions of an integrable discrete reaction-diffusion equation. Physica D 106, 255-269 (1997).
P. C. Bressloff. Neural Networks, Lattice Instantons and the Anti--Integrable Limit. Phys. Rev. Lett. 75, 962-965 (1995).
P. C. Bressloff, V. M. Dwyer and M. J. Kearney. Classical localization and percolation in random environments on trees. Phys. Rev. E 55, 6765-6775 (1997).
M. J. Kearney, V. M. Dwyer and P. C. Bressloff. On the convergence of a class of random geometric series with application to random walks and percolation theory. J. Phys. A 30, L409-414 (1997).
P. C. Bressloff, V. M. Dwyer and M. J. Kearney. A sum-over-paths approach to diffusion on trees. J. Phys. A. 29, 1881-1896 (1996).
V. M. Dwyer, M. J. Kearney, and P. C. Bressloff. An integral equation approach to electromigration under arbitrary time-dependent stress. J. Appl. Phys. 80, 3792-3797 (1996).
P. C. Bressloff, V. M. Dwyer and M. J. Kearney. Classical localization for the drift-diffusion equation on a Cayley tree. J. Phys. A. 29, 6161-6168 (1996).
P. C. Bressloff, V. M. Dwyer and M. J. Kearney. The localization-delocalization transition for drift-diffusion in a random environment. Phys. Rev. Lett. 77, 5075-5078 (1996).