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- Stefanos E. Folias, Paul C. Bressloff
- SIAM J. Applied Dynamical Systems
- 2004

In this paper we show how a local inhomogeneous input can stabilize a stationary-pulse solution in an excitatory neural network. A subsequent reduction of the input amplitude can then induce a Hopf instability of the stationary solution resulting in the formation of a breather. The breather can itself undergo a secondary instability leading to the periodic… (More)

- Stefanos E. Folias, Paul C. Bressloff
- Physical review letters
- 2005

In this Letter we show how nontrivial forms of spatially localized oscillations or breathers can occur in two-dimensional excitable neural media with short-range excitation and long-range inhibition. The basic dynamical mechanism involves a Hopf bifurcation of a stationary pulse solution in the presence of a spatially localized input. Such an input could… (More)

- Stefanos E. Folias, Paul C. Bressloff
- SIAM Journal of Applied Mathematics
- 2005

We analyze the existence and stability of stimulus-locked traveling waves in a onedimensional synaptically coupled excitatory neural network. The network is modeled in terms of a nonlocal integro-differential equation, in which the integral kernel represents the spatial distribution of synaptic weights, and the output firing rate of a neuron is taken to be… (More)

- Paul C. Bressloff, Stefanos E. Folias
- SIAM Journal of Applied Mathematics
- 2004

We show how a one-dimensional excitatory neural network can exhibit a symmetry breaking front bifurcation analogous to that found in reaction diffusion systems. This occurs in a homogeneous network when a stationary front undergoes a pitchfork bifurcation leading to bidirectional wave propagation. We analyze the dynamics in a neighborhood of the front… (More)

- Stefanos E. Folias
- SIAM J. Applied Dynamical Systems
- 2011

- Paul C. Bressloff, Stefanos E. Folias, Alain Prat, Y-X Li
- Physical review letters
- 2003

In this Letter we show that an inhomogeneous input can induce wave propagation failure in an excitatory neural network due to the pinning of a stationary front or pulse solution. A subsequent reduction in the strength of the input can lead to a Hopf instability of the stationary solution resulting in breatherlike oscillatory waves.

- Zachary P. Kilpatrick, Stefanos E. Folias, Paul C. Bressloff
- SIAM J. Applied Dynamical Systems
- 2008

We use averaging and homogenization theory to study the propagation of traveling pulses in an inhomogeneous excitable neural network. The network is modeled in terms of a nonlocal integrodifferential equation, in which the integral kernel represents the spatial distribution of synaptic weights. We show how a spatially periodic modulation of homogeneous… (More)

We study spatiotemporal patterns of activity that emerge in neural fields in the presence of linear adaptation. Using an amplitude equation approach, we show that bifurcations from the homogeneous rest state can lead to a wide variety of stationary and propagating patterns, especially in the case of lateral-inhibitory synaptic weights. Typical solutions are… (More)

- Stefanos E. Folias, Bard Ermentrout
- SIAM J. Applied Dynamical Systems
- 2012

- Stefanos E. Folias, George B Ermentrout
- Physical review letters
- 2011

In this Letter, we study stationary bump solutions in a pair of interacting excitatory-inhibitory (E-I) neural fields in one dimension. We demonstrate the existence of localized bump solutions of persistent activity that can be maintained by the pair of interacting layers when a stationary bump is not supported by either layer in isolation--a scenario which… (More)