Edit Profile (opens in new tab) Bressloff, Paul C. Compute Distance To: Compute Author ID: bressloff.paul-c Published as: Bressloff, Paul C.; Bressloff, P. C.; Bressloff, Paul; Bressloff, Paul C; Bressloff, P. more...less Documents Indexed: 136 Publications since 1989, including 5 Books 2 Contributions as Editor · 1 Further Contribution Co-Authors: 42 Co-Authors with 90 Joint Publications 835 Co-Co-Authors all top 5 Co-Authors 48 single-authored 10 Lawley, Sean D. 7 Coombes, Stephen 7 Taylor, John Gerald 6 Kilpatrick, Zachary P. 6 MacLaurin, James N. 5 Cowan, Jack D. 5 Levien, Ethan 4 Carroll, Samuel R. 4 Dwyer, Vincent M. 4 Folias, Stefanos E. 4 Kearney, Michael J. 3 Fan, Gaoyang 3 Faugeras, Olivier D. 3 Karamched, Bhargav R. 3 Murphy, Patrick 3 Stark, Jaroslav F. 3 Thomas, Peter J. 3 Webber, Matthew A. 3 Xu, Bin 2 Golubitsky, Martin A. 2 Kim, Hyunjoong 2 Lai, Yi Ming 2 Newby, Jay M. 2 Restuccia, Álvaro 1 Bressloff, Neil W. 1 Brooks, Heather A. 1 Brooks, Heather Zinn 1 Carroll, Sam R. 1 Chkhenkeli, S. A. 1 Cornell-Bell, A. H. 1 De Souza, Bruno Lima 1 deGrauw, A. 1 Ditto, William L. 1 Dolan, Kevin 1 Earnshaw, Berton A. 1 Ebersole, J. S. 1 Ermentrout, Bard G. 1 Fokas, Athanassios S. 1 Francis, Joseph T. 1 Galtier, Mathieu N. 1 Gluckman, Bruce J. 1 Hecox, K. 1 Hetling, J. R. 1 Hunter, John D. 1 James, M. P. 1 Jerger, K. K. 1 Jung, Peter 1 Kohrman, M. 1 Li, Yuexian 1 Milton, John G. 1 Moss, Frank E. 1 Netloff, T. I. 1 Nouri-Moghadem, M. 1 Oster, Andrew M. 1 Pecora, Louis M. 1 Prat, Alain 1 Russo, Giovanni 1 Sauer, Timothy D. 1 Schiff, Steven J. 1 Schumm, Ryan D. 1 Spano, Mark L. 1 Strawsburg, R. 1 Towle, Vernon L. 1 Ward, Michael J. 1 Weinstein, S. L. 1 Wiener, Matthew C. 1 Winfree, Arthur Taylor all top 5 Serials 20 Journal of Physics A: Mathematical and Theoretical 17 Physica D 16 SIAM Journal on Applied Mathematics 13 SIAM Journal on Applied Dynamical Systems 8 Journal of Physics A: Mathematical and General 7 Journal of Statistical Mechanics: Theory and Experiment 6 Bulletin of Mathematical Biology 6 Multiscale Modeling & Simulation 5 The Journal of Mathematical Neuroscience 3 Biological Cybernetics 3 Journal of Mathematical Biology 3 Neural Computation 3 Interdisciplinary Applied Mathematics 2 Classical and Quantum Gravity 2 Network (Bristol) 2 Journal of Computational Neuroscience 2 Chaos 1 Journal of Computational Physics 1 Journal of Mathematical Analysis and Applications 1 Nonlinearity 1 Physics Letters. A 1 Neural Networks 1 IEEE Transactions on Systems, Man, and Cybernetics 1 Journal of Nonlinear Science 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Lecture Notes on Mathematical Modelling in the Life Sciences all top 5 Fields 102 Biology and other natural sciences (92-XX) 36 Probability theory and stochastic processes (60-XX) 34 Partial differential equations (35-XX) 24 Statistical mechanics, structure of matter (82-XX) 18 Dynamical systems and ergodic theory (37-XX) 15 Ordinary differential equations (34-XX) 15 Integral equations (45-XX) 12 Quantum theory (81-XX) 10 Computer science (68-XX) 7 Numerical analysis (65-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Systems theory; control (93-XX) 3 General and overarching topics; collections (00-XX) 2 Differential geometry (53-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Combinatorics (05-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 107 Publications have been cited 1,006 times in 546 Documents Cited by ▼ Year ▼ Spatiotemporal dynamics of continuum neural fields. Zbl 1263.92008Bressloff, Paul C. 102 2012 Stochastic processes in cell biology. Zbl 1402.92001Bressloff, Paul C. 68 2014 Breathing pulses in an excitatory neural network. Zbl 1058.92010Folias, Stefanos E.; Bressloff, Paul C. 46 2004 Stochastic neural field theory and the system-size expansion. Zbl 1198.92007Bressloff, Paul C. 41 2009 Traveling fronts and wave propagation failure in an inhomogeneous neural network. Zbl 1004.92005Bressloff, Paul C. 39 2001 Front propagation in stochastic neural fields. Zbl 1246.92004Bressloff, Paul C.; Webber, Matthew A. 32 2012 Stimulus-locked traveling waves and breathers in an excitatory neural network. Zbl 1076.92004Folias, Stefanos E.; Bressloff, Paul C. 27 2005 What geometric visual hallucinations tell us about the visual cortex. Zbl 1037.91083Bressloff, Paul C.; Cowan, Jack D.; Golubitsky, Martin; Thomas, Peter J.; Wiener, Matthew C. 25 2002 Traveling pulses and wave propagation failure in inhomogeneous neural media. Zbl 1159.92010Kilpatrick, Zachary P.; Folias, Stefanos E.; Bressloff, Paul C. 24 2008 Bursting. The genesis of rhythm in the nervous system. Zbl 1094.92500 23 2005 Effects of synaptic depression and adaptation on spatiotemporal dynamics of an excitatory neuronal network. Zbl 1186.92010Kilpatrick, Zachary P.; Bressloff, Paul C. 22 2010 Stochastic switching in biology: from genotype to phenotype. Zbl 1360.92042Bressloff, Paul C. 22 2017 Moment equations for a piecewise deterministic PDE. Zbl 1339.60078Bressloff, Paul C.; Lawley, Sean D. 22 2015 Escape from subcellular domains with randomly switching boundaries. Zbl 1329.82092Bressloff, Paul C.; Lawley, Sean D. 22 2015 Quasi-steady state reduction of molecular motor-based models of directed intermittent search. Zbl 1203.92006Newby, Jay M.; Bressloff, Paul C. 20 2010 Epilepsy as a dynamic disease. Zbl 1058.92027 20 2003 Waves in neural media. From single neurons to neural fields. Zbl 1296.92005Bressloff, Paul C. 19 2014 Metastability in a stochastic neural network modeled as a velocity jump Markov process. Zbl 1278.92005Bressloff, Paul C.; Newby, Jay M. 19 2013 Scalar and pseudoscalar bifurcations motivated by pattern formation on the visual cortex. Zbl 1017.37025Bressloff, Paul C.; Cowan, Jack D.; Golubitsky, Martin; Thomas, Peter J. 16 2001 Front bifurcations in an excitatory neural network. Zbl 1071.92003Bressloff, Paul C.; Folias, Stefanos E. 15 2004 Spatially periodic modulation of cortical patterns by long-range horizontal connections. Zbl 1030.92006Bressloff, Paul C. 15 2003 Escape from a potential well with a randomly switching boundary. Zbl 1405.34050Bressloff, Paul C.; Lawley, Sean D. 15 2015 Two-dimensional bumps in piecewise smooth neural fields with synaptic depression. Zbl 1221.92017Bressloff, Paul C.; Kilpatrick, Zachary P. 14 2011 Symmetry and phase-locking in a ring of pulse-coupled oscillators with distributed delays. Zbl 0937.34060Bressloff, P. C.; Coombes, S. 14 1999 Diffusion in cells with stochastically gated gap junctions. Zbl 1351.82056Bressloff, Paul C. 13 2016 Nonlinear Langevin equations for wandering patterns in stochastic neural fields. Zbl 1402.92076Bressloff, Paul C.; Kilpatrick, Zachary P. 13 2015 Diffusion on a tree with stochastically gated nodes. Zbl 1342.92073Bressloff, Paul C.; Lawley, Sean D. 12 2016 An amplitude equation approach to contextual effects in visual cortex. Zbl 0987.92005Bressloff, Paul C.; Cowan, Jack D. 12 2002 Binocular rivalry in a competitive neural network with synaptic depression. Zbl 1202.92013Kilpatrick, Zachary P.; Bressloff, Paul C. 11 2010 Weakly interacting pulses in synaptically coupled neural media. Zbl 1091.92013Bressloff, Paul C. 11 2005 A variational method for analyzing stochastic limit cycle oscillators. Zbl 1409.60101Bressloff, Paul C.; MacLaurin, James N. 10 2018 The visual cortex as a crystal. Zbl 1017.92009Bressloff, Paul C.; Cowan, Jack D. 10 2002 Spontaneous symmetry breaking in self-organizing neural fields. Zbl 1129.92010Bressloff, Paul C. 10 2005 Travelling waves in chains of pulse-coupled integrate-and-fire oscillators with distributed delays. Zbl 0934.34057Bressloff, P. C.; Coombes, S. 10 1999 Path-integral methods for analyzing the effects of fluctuations in stochastic hybrid neural networks. Zbl 1361.92005Bressloff, Paul C. 9 2015 Inhomogeneity-induced bifurcation of stationary and oscillatory pulses. Zbl 1082.35025Prat, Alain; Li, Yue-Xian; Bressloff, Paul 9 2005 Stability of bumps in piecewise smooth neural fields with nonlinear adaptation. Zbl 1189.37027Kilpatrick, Zachary P.; Bressloff, Paul C. 9 2010 A dynamical theory of spike train transitions in networks of integrate-and-fire oscillators. Zbl 0947.34022Bressloff, P. C.; Coombes, S. 9 2000 Traveling waves and pulses in a one-dimensional network of excitable integrate-and-fire neurons. Zbl 0952.92007Bressloff, Paul C. 8 2000 Dynamically active compartments coupled by a stochastically gated gap junction. Zbl 1379.35332Bressloff, Paul C.; Lawley, Sean D. 7 2017 Dynamics of a compartmental model integrate-and-fire neuron with somatic potential reset. Zbl 0885.65155Bressloff, Paul C. 7 1995 Solitary waves in a model of dendritic cable with active spines. Zbl 1016.92004Coombes, S.; Bressloff, P. C. 7 2000 Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise. Zbl 1259.92004Bressloff, Paul C; Lai, Yi Ming 7 2011 A PDE-DDE model for cell polarization in fission yeast. Zbl 1346.92024Xu, Bin; Bressloff, Paul C. 6 2016 From invasion to extinction in heterogeneous neural fields. Zbl 1291.92024Bressloff, Paul C. 6 2012 Euclidean shift-twist symmetry in population models of self-aligning objects. Zbl 1051.92002Bressloff, Paul C. 6 2004 Aggregation-fragmentation model of vesicular transport in neurons. Zbl 1342.92039Bressloff, Paul C. 5 2016 Model of reversible vesicular transport with exclusion. Zbl 1348.92032Bressloff, Paul C.; Karamched, Bhargav R. 5 2016 Compartmental-model response function for dendritic trees. Zbl 0800.92034Bressloff, Paul C.; Taylor, John G. 5 1993 Synchronization of stochastic hybrid oscillators driven by a common switching environment. Zbl 1404.34072Bressloff, Paul C.; MacLaurin, James 5 2018 A developmental model of ocular dominance column formation on a growing cortex. Zbl 1334.92043Oster, Andrew M.; Bressloff, Paul C. 5 2006 A mechanism for Turing pattern formation with active and passive transport. Zbl 1347.92012Brooks, Heather A.; Bressloff, Paul C. 4 2016 Diffusion of protein receptors on a cylindrical dendritic membrane with partially absorbing traps. Zbl 1146.92005Bressloff, Paul C.; Earnshaw, Berton A.; Ward, Michael J. 4 2008 A ‘sum-over-paths’ approach to diffusion on stress. Zbl 0902.60063Bressloff, Paul C.; Dwyer, V. M.; Kearney, M. J. 4 1996 Residence times of a Brownian particle with temporal heterogeneity. Zbl 1374.60158Bressloff, Paul C.; Lawley, Sean D. 4 2017 On the Hamiltonian structure of large deviations in stochastic hybrid systems. Zbl 1457.82190Bressloff, Paul C.; Faugeras, Olivier 4 2017 Stochastic active-transport model of cell polarization. Zbl 1346.92022Bressloff, Paul C.; Xu, Bin 4 2015 A stochastic hybrid framework for obtaining statistics of many random walkers in a switching environment. Zbl 1356.35264Levien, Ethan; Bressloff, Paul C. 4 2016 Node-to-node and node-to-medium synchronization in quorum sensing networks affected by state-dependent noise. Zbl 1432.93314Fan, Gaoyang; Russo, Giovanni; Bressloff, Paul C. 3 2019 Effective permeability of a gap junction with age-structured switching. Zbl 1431.92041Bressloff, Paul C.; Lawley, Sean D.; Murphy, Patrick 3 2020 Analysis of associative reinforcement learning in neural networks using iterated function systems. Zbl 0776.92002Bressloff, Paul C.; Stark, Jaroslav 3 1992 A variational method for analyzing limit cycle oscillations in stochastic hybrid systems. Zbl 1394.92049Bressloff, Paul C.; MacLaurin, James 3 2018 On balance relations for irreversible chemical reaction networks. Zbl 1432.82018Levien, Ethan; Bressloff, Paul C. 3 2017 Population model of quorum sensing with multiple parallel pathways. Zbl 1382.92125Fan, Gaoyang; Bressloff, Paul C. 3 2017 Propagation of extrinsic fluctuations in biochemical birth-death processes. Zbl 1415.92079Bressloff, P. C.; Levien, E. 3 2019 Iterated function systems and their applications. Zbl 0827.28006Stark, J.; Bressloff, P. 3 1993 Spontaneous pattern formation in primary visual cortex. Zbl 1132.92309Bressloff, Paul C.; Cowan, Jack D. 3 2003 Effects of cell geometry on reversible vesicular transport. Zbl 1357.92023Karamched, Bhargav R.; Bressloff, Paul C. 3 2017 Resonantlike synchronization and bursting in a model of pulse-coupled neurons with active dendrites. Zbl 0926.92007Bressloff, Paul C. 3 1999 Lectures in mathematical neuroscience. Zbl 1352.92024Bressloff, Paul C. 3 2009 Stochastic dynamics of reinforcement learning. Zbl 0839.68081Bressloff, P. C. 3 1995 Target competition for resources under multiple search-and-capture events with stochastic resetting. Zbl 1472.60149Bressloff, P. C. 3 2020 Direct vs. synaptic coupling in a mathematical model of cytoneme-based morphogen gradient formation. Zbl 1398.92030Kim, Hyunjoong; Bressloff, Paul C. 2 2018 Spatiotemporal dynamics of neural fields on product spaces. Zbl 1322.92007Bressloff, Paul C.; Carroll, Samuel R. 2 2014 Two-state representations of three-state neural networks. Zbl 0727.68103Stark, Jaroslav; Bressloff, Paul 2 1990 Stochastic hybrid systems in cellular neuroscience. Zbl 1405.92037Bressloff, Paul C.; Maclaurin, James N. 2 2018 Symmetric bifurcations in a neural field model for encoding the direction of spatial contrast gradients. Zbl 1385.92012Carroll, Samuel R.; Bressloff, Paul C. 2 2018 Exact travlling wavelling wave solutions of an ”intgrablegrable” discrete reaction-diffusion equation. Zbl 0943.37036Bressloff, P. C.; Rowlands, G. 2 1997 Propagation of CaMKII translocation waves in heterogeneous spiny dendrites. Zbl 1402.92075Bressloff, Paul C. 2 2013 Hebbian learning of recurrent connections: a geometrical perspective. Zbl 1269.92005Galtier, Mathieu N.; Faugeras, Olivier D.; Bressloff, Paul C. 2 2012 A Green’s function approach to analysing the effects of random synaptic background activity in a model neural network. Zbl 0939.68774Bressloff, P. C. 2 1994 Phase equation for patterns of orientation selectivity in a neural field model of visual cortex. Zbl 1343.92079Carroll, Samuel R.; Bressloff, Paul C. 2 2016 Drift-diffusion on a Cayley tree with stochastic resetting: the localization-delocalization transition. Zbl 07382823Bressloff, Paul C. 2 2021 Wandering bumps in a stochastic neural field: a variational approach. Zbl 1493.92005MacLaurin, James N.; Bressloff, Paul C. 2 2020 Phase reduction of stochastic biochemical oscillators. Zbl 1433.92015Bressloff, Paul C.; MacLaurin, James N. 1 2020 Perceptron-like learning in time-summating neural networks. Zbl 0764.92004Bressloff, Paul C.; Taylor, John G. 1 1992 Temporal processing in neural networks with adaptive short term memory: A compartmental model approach. Zbl 0772.92001Bressloff, Paul C. 1 1993 Low firing-rates in a compartmental model neuron. Zbl 0771.92006Bressloff, Paul C.; Taylor, John G. 1 1993 Coupling sample paths to the thermodynamic limit in Monte Carlo estimators with applications to gene expression. Zbl 1378.65023Levien, Ethan; Bressloff, Paul C. 1 2017 Neural field model of binocular rivalry waves. Zbl 1446.92034Bressloff, Paul C.; Webber, Matthew A. 1 2012 Modeling the role of feedback in the adaptive response of bacterial quorum sensing. Zbl 1415.92071Fan, Gaoyang; Bressloff, Paul C. 1 2019 Average firing rate of a neural network with dynamical disorder. Zbl 0839.68080Bressloff, Paul C. 1 1995 Dynamics of compartmental model neurons. Zbl 0812.92004Bressloff, Paul C.; Taylor, John G. 1 1994 Robustness of stochastic chemical reaction networks to extrinsic noise: the role of deficiency. Zbl 1400.92211Levien, Ethan; Bressloff, Paul C. 1 2018 Diffusion in an age-structured randomly switching environment. Zbl 1400.92426Bressloff, Paul C.; Lawley, Sean D.; Murphy, Patrick 1 2018 A theory of synchrony for active compartments with delays coupled through bulk diffusion. Zbl 1384.92032Xu, Bin; Bressloff, Paul C. 1 2017 Doubly stochastic Poisson model of flagellar length control. Zbl 1459.82222Bressloff, Paul C.; Karamched, Bhargav R. 1 2018 Neural pattern formation in networks with dendritic structure. Zbl 0935.92009Bressloff, P. C.; De Souza, B. 1 1998 Burgers’ equation on a branching structure. Zbl 1043.35512Bressloff, P. C.; Dwyer, V. M.; Kearney, M. J. 1 1997 A new Green’s function method for solving linear PDE’s in two variables. Zbl 0881.65092Bressloff, Paul C. 1 1997 Drift-diffusion on a Cayley tree with stochastic resetting: the localization-delocalization transition. Zbl 07382823Bressloff, Paul C. 2 2021 Asymptotic analysis of target fluxes in the three-dimensional narrow capture problem. Zbl 1465.35027Bressloff, Paul C. 1 2021 Coherent spin states and stochastic hybrid path integrals. Zbl 07356466Bressloff, Paul C. 1 2021 Effective permeability of a gap junction with age-structured switching. Zbl 1431.92041Bressloff, Paul C.; Lawley, Sean D.; Murphy, Patrick 3 2020 Target competition for resources under multiple search-and-capture events with stochastic resetting. Zbl 1472.60149Bressloff, P. C. 3 2020 Wandering bumps in a stochastic neural field: a variational approach. Zbl 1493.92005MacLaurin, James N.; Bressloff, Paul C. 2 2020 Phase reduction of stochastic biochemical oscillators. Zbl 1433.92015Bressloff, Paul C.; MacLaurin, James N. 1 2020 Node-to-node and node-to-medium synchronization in quorum sensing networks affected by state-dependent noise. Zbl 1432.93314Fan, Gaoyang; Russo, Giovanni; Bressloff, Paul C. 3 2019 Propagation of extrinsic fluctuations in biochemical birth-death processes. Zbl 1415.92079Bressloff, P. C.; Levien, E. 3 2019 Modeling the role of feedback in the adaptive response of bacterial quorum sensing. Zbl 1415.92071Fan, Gaoyang; Bressloff, Paul C. 1 2019 A variational method for analyzing stochastic limit cycle oscillators. Zbl 1409.60101Bressloff, Paul C.; MacLaurin, James N. 10 2018 Synchronization of stochastic hybrid oscillators driven by a common switching environment. Zbl 1404.34072Bressloff, Paul C.; MacLaurin, James 5 2018 A variational method for analyzing limit cycle oscillations in stochastic hybrid systems. Zbl 1394.92049Bressloff, Paul C.; MacLaurin, James 3 2018 Direct vs. synaptic coupling in a mathematical model of cytoneme-based morphogen gradient formation. Zbl 1398.92030Kim, Hyunjoong; Bressloff, Paul C. 2 2018 Stochastic hybrid systems in cellular neuroscience. Zbl 1405.92037Bressloff, Paul C.; Maclaurin, James N. 2 2018 Symmetric bifurcations in a neural field model for encoding the direction of spatial contrast gradients. Zbl 1385.92012Carroll, Samuel R.; Bressloff, Paul C. 2 2018 Robustness of stochastic chemical reaction networks to extrinsic noise: the role of deficiency. Zbl 1400.92211Levien, Ethan; Bressloff, Paul C. 1 2018 Diffusion in an age-structured randomly switching environment. Zbl 1400.92426Bressloff, Paul C.; Lawley, Sean D.; Murphy, Patrick 1 2018 Doubly stochastic Poisson model of flagellar length control. Zbl 1459.82222Bressloff, Paul C.; Karamched, Bhargav R. 1 2018 Stochastic switching in biology: from genotype to phenotype. Zbl 1360.92042Bressloff, Paul C. 22 2017 Dynamically active compartments coupled by a stochastically gated gap junction. Zbl 1379.35332Bressloff, Paul C.; Lawley, Sean D. 7 2017 Residence times of a Brownian particle with temporal heterogeneity. Zbl 1374.60158Bressloff, Paul C.; Lawley, Sean D. 4 2017 On the Hamiltonian structure of large deviations in stochastic hybrid systems. Zbl 1457.82190Bressloff, Paul C.; Faugeras, Olivier 4 2017 On balance relations for irreversible chemical reaction networks. Zbl 1432.82018Levien, Ethan; Bressloff, Paul C. 3 2017 Population model of quorum sensing with multiple parallel pathways. Zbl 1382.92125Fan, Gaoyang; Bressloff, Paul C. 3 2017 Effects of cell geometry on reversible vesicular transport. Zbl 1357.92023Karamched, Bhargav R.; Bressloff, Paul C. 3 2017 Coupling sample paths to the thermodynamic limit in Monte Carlo estimators with applications to gene expression. Zbl 1378.65023Levien, Ethan; Bressloff, Paul C. 1 2017 A theory of synchrony for active compartments with delays coupled through bulk diffusion. Zbl 1384.92032Xu, Bin; Bressloff, Paul C. 1 2017 Mean first passage times for piecewise deterministic Markov processes and the effects of critical points. Zbl 1456.60184Bressloff, Paul C.; Lawley, Sean D. 1 2017 Diffusion in cells with stochastically gated gap junctions. Zbl 1351.82056Bressloff, Paul C. 13 2016 Diffusion on a tree with stochastically gated nodes. Zbl 1342.92073Bressloff, Paul C.; Lawley, Sean D. 12 2016 A PDE-DDE model for cell polarization in fission yeast. Zbl 1346.92024Xu, Bin; Bressloff, Paul C. 6 2016 Aggregation-fragmentation model of vesicular transport in neurons. Zbl 1342.92039Bressloff, Paul C. 5 2016 Model of reversible vesicular transport with exclusion. Zbl 1348.92032Bressloff, Paul C.; Karamched, Bhargav R. 5 2016 A mechanism for Turing pattern formation with active and passive transport. Zbl 1347.92012Brooks, Heather A.; Bressloff, Paul C. 4 2016 A stochastic hybrid framework for obtaining statistics of many random walkers in a switching environment. Zbl 1356.35264Levien, Ethan; Bressloff, Paul C. 4 2016 Phase equation for patterns of orientation selectivity in a neural field model of visual cortex. Zbl 1343.92079Carroll, Samuel R.; Bressloff, Paul C. 2 2016 Moment equations for a piecewise deterministic PDE. Zbl 1339.60078Bressloff, Paul C.; Lawley, Sean D. 22 2015 Escape from subcellular domains with randomly switching boundaries. Zbl 1329.82092Bressloff, Paul C.; Lawley, Sean D. 22 2015 Escape from a potential well with a randomly switching boundary. Zbl 1405.34050Bressloff, Paul C.; Lawley, Sean D. 15 2015 Nonlinear Langevin equations for wandering patterns in stochastic neural fields. Zbl 1402.92076Bressloff, Paul C.; Kilpatrick, Zachary P. 13 2015 Path-integral methods for analyzing the effects of fluctuations in stochastic hybrid neural networks. Zbl 1361.92005Bressloff, Paul C. 9 2015 Stochastic active-transport model of cell polarization. Zbl 1346.92022Bressloff, Paul C.; Xu, Bin 4 2015 Stochastic processes in cell biology. Zbl 1402.92001Bressloff, Paul C. 68 2014 Waves in neural media. From single neurons to neural fields. Zbl 1296.92005Bressloff, Paul C. 19 2014 Spatiotemporal dynamics of neural fields on product spaces. Zbl 1322.92007Bressloff, Paul C.; Carroll, Samuel R. 2 2014 Binocular rivalry waves in a directionally selective neural field model. Zbl 1349.91240Carroll, Samuel R.; Bressloff, Paul C. 1 2014 Metastability in a stochastic neural network modeled as a velocity jump Markov process. Zbl 1278.92005Bressloff, Paul C.; Newby, Jay M. 19 2013 Propagation of CaMKII translocation waves in heterogeneous spiny dendrites. Zbl 1402.92075Bressloff, Paul C. 2 2013 Dispersal and noise: various modes of synchrony in ecological oscillators. Zbl 1279.92084Bressloff, Paul C.; Lai, Yi Ming 1 2013 Spatiotemporal dynamics of continuum neural fields. Zbl 1263.92008Bressloff, Paul C. 102 2012 Front propagation in stochastic neural fields. Zbl 1246.92004Bressloff, Paul C.; Webber, Matthew A. 32 2012 From invasion to extinction in heterogeneous neural fields. Zbl 1291.92024Bressloff, Paul C. 6 2012 Hebbian learning of recurrent connections: a geometrical perspective. Zbl 1269.92005Galtier, Mathieu N.; Faugeras, Olivier D.; Bressloff, Paul C. 2 2012 Neural field model of binocular rivalry waves. Zbl 1446.92034Bressloff, Paul C.; Webber, Matthew A. 1 2012 Two-dimensional bumps in piecewise smooth neural fields with synaptic depression. Zbl 1221.92017Bressloff, Paul C.; Kilpatrick, Zachary P. 14 2011 Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise. Zbl 1259.92004Bressloff, Paul C; Lai, Yi Ming 7 2011 Effects of synaptic depression and adaptation on spatiotemporal dynamics of an excitatory neuronal network. Zbl 1186.92010Kilpatrick, Zachary P.; Bressloff, Paul C. 22 2010 Quasi-steady state reduction of molecular motor-based models of directed intermittent search. Zbl 1203.92006Newby, Jay M.; Bressloff, Paul C. 20 2010 Binocular rivalry in a competitive neural network with synaptic depression. Zbl 1202.92013Kilpatrick, Zachary P.; Bressloff, Paul C. 11 2010 Stability of bumps in piecewise smooth neural fields with nonlinear adaptation. Zbl 1189.37027Kilpatrick, Zachary P.; Bressloff, Paul C. 9 2010 Stochastic neural field theory and the system-size expansion. Zbl 1198.92007Bressloff, Paul C. 41 2009 Lectures in mathematical neuroscience. Zbl 1352.92024Bressloff, Paul C. 3 2009 Traveling pulses and wave propagation failure in inhomogeneous neural media. Zbl 1159.92010Kilpatrick, Zachary P.; Folias, Stefanos E.; Bressloff, Paul C. 24 2008 Diffusion of protein receptors on a cylindrical dendritic membrane with partially absorbing traps. Zbl 1146.92005Bressloff, Paul C.; Earnshaw, Berton A.; Ward, Michael J. 4 2008 A developmental model of ocular dominance column formation on a growing cortex. Zbl 1334.92043Oster, Andrew M.; Bressloff, Paul C. 5 2006 Stimulus-locked traveling waves and breathers in an excitatory neural network. Zbl 1076.92004Folias, Stefanos E.; Bressloff, Paul C. 27 2005 Bursting. The genesis of rhythm in the nervous system. Zbl 1094.92500 23 2005 Weakly interacting pulses in synaptically coupled neural media. Zbl 1091.92013Bressloff, Paul C. 11 2005 Spontaneous symmetry breaking in self-organizing neural fields. Zbl 1129.92010Bressloff, Paul C. 10 2005 Inhomogeneity-induced bifurcation of stationary and oscillatory pulses. Zbl 1082.35025Prat, Alain; Li, Yue-Xian; Bressloff, Paul 9 2005 Breathing pulses in an excitatory neural network. Zbl 1058.92010Folias, Stefanos E.; Bressloff, Paul C. 46 2004 Front bifurcations in an excitatory neural network. Zbl 1071.92003Bressloff, Paul C.; Folias, Stefanos E. 15 2004 Euclidean shift-twist symmetry in population models of self-aligning objects. Zbl 1051.92002Bressloff, Paul C. 6 2004 Epilepsy as a dynamic disease. Zbl 1058.92027 20 2003 Spatially periodic modulation of cortical patterns by long-range horizontal connections. Zbl 1030.92006Bressloff, Paul C. 15 2003 Spontaneous pattern formation in primary visual cortex. Zbl 1132.92309Bressloff, Paul C.; Cowan, Jack D. 3 2003 What geometric visual hallucinations tell us about the visual cortex. Zbl 1037.91083Bressloff, Paul C.; Cowan, Jack D.; Golubitsky, Martin; Thomas, Peter J.; Wiener, Matthew C. 25 2002 An amplitude equation approach to contextual effects in visual cortex. Zbl 0987.92005Bressloff, Paul C.; Cowan, Jack D. 12 2002 The visual cortex as a crystal. Zbl 1017.92009Bressloff, Paul C.; Cowan, Jack D. 10 2002 Traveling fronts and wave propagation failure in an inhomogeneous neural network. Zbl 1004.92005Bressloff, Paul C. 39 2001 Scalar and pseudoscalar bifurcations motivated by pattern formation on the visual cortex. Zbl 1017.37025Bressloff, Paul C.; Cowan, Jack D.; Golubitsky, Martin; Thomas, Peter J. 16 2001 A dynamical theory of spike train transitions in networks of integrate-and-fire oscillators. Zbl 0947.34022Bressloff, P. C.; Coombes, S. 9 2000 Traveling waves and pulses in a one-dimensional network of excitable integrate-and-fire neurons. Zbl 0952.92007Bressloff, Paul C. 8 2000 Solitary waves in a model of dendritic cable with active spines. Zbl 1016.92004Coombes, S.; Bressloff, P. C. 7 2000 Symmetry and phase-locking in a ring of pulse-coupled oscillators with distributed delays. Zbl 0937.34060Bressloff, P. C.; Coombes, S. 14 1999 Travelling waves in chains of pulse-coupled integrate-and-fire oscillators with distributed delays. Zbl 0934.34057Bressloff, P. C.; Coombes, S. 10 1999 Resonantlike synchronization and bursting in a model of pulse-coupled neurons with active dendrites. Zbl 0926.92007Bressloff, Paul C. 3 1999 A new spectral transform for solving the continuous and spatially discrete heat equations on simple trees. Zbl 0932.35033Bressloff, P. C.; Fokas, A. S. 1 1999 Neural pattern formation in networks with dendritic structure. Zbl 0935.92009Bressloff, P. C.; De Souza, B. 1 1998 Exact travlling wavelling wave solutions of an ”intgrablegrable” discrete reaction-diffusion equation. Zbl 0943.37036Bressloff, P. C.; Rowlands, G. 2 1997 Burgers’ equation on a branching structure. Zbl 1043.35512Bressloff, P. C.; Dwyer, V. M.; Kearney, M. J. 1 1997 A new Green’s function method for solving linear PDE’s in two variables. Zbl 0881.65092Bressloff, Paul C. 1 1997 A ‘sum-over-paths’ approach to diffusion on stress. Zbl 0902.60063Bressloff, Paul C.; Dwyer, V. M.; Kearney, M. J. 4 1996 Classical localization for the drift-diffusion equation on a Cayley tree. Zbl 0905.35039Bressloff, Paul C.; Dwyer, Vincent M.; Kearney, Michael J. 1 1996 Dynamics of a compartmental model integrate-and-fire neuron with somatic potential reset. Zbl 0885.65155Bressloff, Paul C. 7 1995 Stochastic dynamics of reinforcement learning. Zbl 0839.68081Bressloff, P. C. 3 1995 Average firing rate of a neural network with dynamical disorder. Zbl 0839.68080Bressloff, Paul C. 1 1995 A Green’s function approach to analysing the effects of random synaptic background activity in a model neural network. Zbl 0939.68774Bressloff, P. C. 2 1994 Dynamics of compartmental model neurons. Zbl 0812.92004Bressloff, Paul C.; Taylor, John G. 1 1994 ...and 7 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 808 Authors 58 Bressloff, Paul C. 24 Lawley, Sean D. 20 Coombes, Stephen 17 Kilpatrick, Zachary P. 13 Wyller, John A. 12 Laing, Carlo R. 11 Faugeras, Olivier D. 10 MacLaurin, James N. 9 Faye, Grégory 9 Hutt, Axel 9 Ward, Michael J. 8 Hupkes, Hermen Jan 8 Robinson, Peter A. 6 Bokes, Pavol 6 Duan, Jinqiao 6 Ermentrout, Bard G. 6 Kühn, Christian 6 Oleynik, Anna 6 Sarti, Alessandro 5 Chossat, Pascal 5 Citti, Giovanna 5 Keener, James P. 5 Longtin, André 5 Ponosov, Arkadiĭ Vladimirovich 5 Thomas, Peter J. 5 Touboul, Jonathan David 4 beim Graben, Peter 4 Campbell, Sue Ann 4 Chaillet, Antoine 4 Cowan, Jack D. 4 Einevoll, Gaute T. 4 Ermentrout, George Bard 4 Hamster, C. H. S. 4 Kurths, Jürgen 4 Lai, Yi Ming 4 Levien, Ethan 4 Lewis, Mark Alun 4 Li, Yuexian 4 Lima, Pedro Miguel 4 Miles, Christopher E. 4 Poll, Daniel B. 4 Potthast, Roland W. E. 4 Thul, Rüdiger 4 Wilson, Dan D. 4 Xu, Bin 4 Zhang, Linghai 3 Amari, Shun-ichi 3 Avitabile, Daniele 3 Burlakov, Evgenii O. 3 Carroll, Samuel R. 3 de Vries, Gerda 3 Detorakis, Georgios Is. 3 Drysdale, P. M. 3 Dumont, Grégory 3 Fung, C. C. Alan 3 Gou, Jia 3 Horikawa, Yo 3 Huang, Zhehao 3 Jaramillo, Gabriela 3 Karamched, Bhargav R. 3 Kofané, Timoléon Crépin 3 Kolodina, Karina 3 Kolokolnikov, Theodore 3 Kulikov, Gennady Yur’evich 3 Li, Xiaofan 3 Liu, Zhengrong 3 Lord, Gabriel James 3 Murphy, Patrick 3 Nishiura, Yasumasa 3 Reed, Michael C. 3 Rougier, Nicolas P. 3 Rubin, Jonathan E. 3 Schmidt, Helmut 3 Schouten-Straatman, Willem M. 3 Stannat, Wilhelm 3 van Albada, S. J. 3 Veltz, Romain 2 Ahn, Sungwoo 2 Ashwin, Peter 2 Baccelli, François Louis 2 Barreiro, Andrea K. 2 Bertalmío, Marcelo 2 Blomquist, Patrick 2 Bojak, Ingo 2 Brackley, Chris A. 2 Cabana, Tanguy 2 Carroll, Sam R. 2 Chen, Xiaoli 2 Cheng, Xiujun 2 Chevallier, Julien 2 Chowdhury, Debashish 2 Ciocanel, Maria-Veronica 2 Crevat, Joachim 2 Dyson, Alan 2 Edelstein-Keshet, Leah 2 Erlhagen, Wolfram 2 Fan, Gaoyang 2 Fasoli, Diego 2 Favali, Marta 2 Fetecau, Razvan C. ...and 708 more Authors all top 5 Cited in 115 Serials 56 Physica D 34 The Journal of Mathematical Neuroscience 33 Journal of Mathematical Biology 29 SIAM Journal on Applied Dynamical Systems 23 Biological Cybernetics 23 Bulletin of Mathematical Biology 23 Chaos 22 SIAM Journal on Applied Mathematics 22 Journal of Computational Neuroscience 15 Neural Computation 13 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 13 Journal of Theoretical Biology 9 Multiscale Modeling & Simulation 9 Journal of Statistical Mechanics: Theory and Experiment 8 Journal of Nonlinear Science 8 Discrete and Continuous Dynamical Systems. 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Real World Applications 1 Journal of Evolution Equations 1 Communications on Pure and Applied Analysis 1 Advances in Difference Equations 1 Stochastics ...and 15 more Serials all top 5 Cited in 38 Fields 398 Biology and other natural sciences (92-XX) 163 Partial differential equations (35-XX) 129 Probability theory and stochastic processes (60-XX) 76 Ordinary differential equations (34-XX) 76 Dynamical systems and ergodic theory (37-XX) 55 Integral equations (45-XX) 42 Numerical analysis (65-XX) 42 Statistical mechanics, structure of matter (82-XX) 25 Systems theory; control (93-XX) 20 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 14 Computer science (68-XX) 11 Operator theory (47-XX) 9 Combinatorics (05-XX) 8 Statistics (62-XX) 8 Operations research, mathematical programming (90-XX) 6 Mechanics of particles and systems (70-XX) 5 Functional analysis (46-XX) 4 Approximations and expansions (41-XX) 4 Fluid mechanics (76-XX) 4 Quantum theory (81-XX) 3 Integral transforms, operational calculus (44-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Mechanics of deformable solids (74-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 General and overarching topics; collections (00-XX) 2 Special functions (33-XX) 2 Difference and functional equations (39-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Geophysics (86-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Convex and discrete geometry (52-XX) 1 Optics, electromagnetic theory (78-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year