Supported by NSF through grant DMS 1311414.

^{§}undergraduate student.

## Submitted

*-*J. Crevat, G. Faye and F. Filbet

**Rigorous derivation of the nonlocal reaction-diffusion FitzHugh-Nagumo system.**(PDF)

*-*G. Faye and Z.P. Kilpatrick

**Threshold of front propagation in neural fields: An interface dynamics approach.**(PDF)

*-*G. Faye and M. Holzer

**Asymptotic stability of the critical Fisher-KPP front using pointwise estimates.**(PDF)

*-*G. Faye and M. Holzer

**Bifurcation to locked fronts in two component reaction-diffusion systems.**(PDF)

## Publications

*-*G. Faye

**Traveling fronts for lattice neural field equations.**(PDF)

Physica D, to appear (2018), pp. 1-31.

*-*G. Faye and G. Peltier

^{§}

**Anomalous invasion speed in a system of coupled reaction-diffusion equations.**(PDF)

Commun. Math. Sci., Vol. 16, No. 2 (2018), pp. 441-461.

*-*G. Faye, M. Holzer and A. Scheel

**Linear spreading speeds from nonlinear resonant interaction.**(PDF)

Nonlinearity, vol 30, no 6, (2017), pp. 2403-2442.

*-*G. Faye and A. Scheel

**Center Manifolds without a Phase Space.**(PDF)

Trans. Amer. Math. Soc., 370 (2018), 5843-5885.

*-*J. Fang and G. Faye

**Monotone traveling waves for delayed neural field equations.**(PDF)

Mathematical Methods & Models in Applied Sciences, vol 26, no 10 (2016), pp. 1919-1954.

*-*T. Andreson

^{§}, G. Faye, A. Scheel and D. Stauffer

^{§}

**Pinning and Unpinning in Nonlocal Systems.**(PDF)

Journal of Dynamics and Differential Equations, vol 28, issue 3-4, (2016), pp 897-923.

*-*G. Faye

**Multidimensional stability of planar traveling waves for the scalar nonlocal Allen-Cahn equation.**(PDF)

Discrete and Continuous Dynamical System A, volume 36, no. 5 (2016), pp. 2473-2496.

*-*G. Faye and M. Holzer

**Modulated traveling fronts for a nonlocal Fisher-KPP equation: a dynamical system approach.**(PDF)

J. of Differential Equations, Volume 258, Issue 7, (2015), pp. 2257–2289.

*-*G. Faye and A. Scheel

**Existence of pulses in excitable media with nonlocal coupling.**(PDF)

Advances in Mathematics, vol 270 (2015), pp. 400-456.

*-*C. Browne

^{§}and A.L. Dickerson

^{§}- Mentors: G. Faye and A. Scheel

**Coherent Structures in Scalar Feed-Forward Chains.**(PDF)

SIAM Undergraduate Research Online, vol 7 (2014), pp. 306-329.

*-*G. Faye and A. Scheel

**Fredholm properties of nonlocal differential equations via spectral flow.**(PDF)

Indiana Univ. Math. J., 63 (2014), pp. 1311-1348.

*-*G. Faye and J. Touboul

**Pulsatile localized dynamics in delayed neural-field equations.**(PDF)

SIAM J. Appl. Math. 74-5 (2014), pp. 1657-1690.

*-*Z. Kilpatrick and G. Faye

**Pulse bifurcations in stochastic neural fields.**(PDF)

SIAM J. Appl. Dyn. Syst., 13(2) (2014), pp. 830-860.

*-*J. Rankin, D. Avitabile, J. Baladron, G. Faye and D.J. Lloyd

**Continuation of localised coherent structures in nonlocal neural field equations.**(PDF)

SIAM J. Sci. Comput. 36-1 (2014), pp. B70-B93.

*-*G. Faye

**Existence and stability of traveling pulses of a neural field equation with synaptic depression.**(PDF)

SIAM J. Appl. Dyn. Syst., 12-4 (2013), pp. 2032-2067.

*-*P. Chossat and G. Faye

**Pattern formation for the Swift-Hohenberg equation on the hyperbolic plane**(PDF)

Journal of Dynamics and Differential Equations, vol 27, Issue 3, (2015), pp. 485-531.

*-*G. Faye and P. Chossat

**A spatialized model of textures perception using structure tensor formalism**(PDF)

Networks and Heterogeneous Media, vol 8, issue 1, (2013), pp 211-260

*-*G. Faye, J. Rankin and D.J. Lloyd

**Localized radial bumps of a neural field equation on the Euclidean plane and the Poincaré disk**(PDF)

Nonlinearity, 26, (2013), pp 437-478

*-*G. Faye, J. Rankin and P. Chossat

**Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis**(PDF)

Journal of Mathematical Biology, (2013), vol 66, issue 6, pp 1303-1338

*-*G. Faye

**Reduction method for studying localized solutions of neural field equations on the Poincaré disk**(PDF)

C. R. Math. Acad. Sci. Paris, vol 350, issue 3-4, (2012), pp 161-166

*-*G. Faye and P. Chossat

**Bifurcation diagrams and heteroclinic networks of octagonal H-planforms**(PDF)

Journal of Nonlinear Science, vol 22, issue 3, (2012), pp 277-325

*-*G. Faye, P. Chossat and O. Faugeras

**Analysis of a hyperbolic geometric model for visual texture perception**(PDF)

Journal of Mathematical Neuroscience, 1(4), (2011)

*-*P. Chossat, G. Faye and O. Faugeras

**Bifurcation of Hyperbolic Planforms**(PDF)

Journal of Nonlinear Science,vol 21, issue 4, (2011), pp 465-498

*-*G. Faye and O. Faugeras

**Some theoretical and numerical results for delayed neural field equations**(PDF)

Physica D,vol 239, issue 9, (2010), pp 561-578

## PhD manuscript

G. Faye

**-**

**Symmetry breaking and pattern formation in some neural field equations**(PDF)