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 bifurcation using perturbation methods, and we establish that a weak input inhomogeneity can induce a Hopf instability of the stationary front, leading to the formation of an oscillatory front or breather. We then carry out a stability analysis of stationary fronts in an exactly solvable model and use this to derive conditions for oscillatory fronts beyond the weak input regime. In particular,...
In this Letter we show that an inhomogeneous input can induce wave propagation failure in an excitat...
Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. ...
Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. ...
In this thesis methods from nonlinear dynamical systems, pattern formation and bifurcation theory, c...
Fronts are travelling waves in spatially extended systems that connect two different spatially homog...
Fronts are travelling waves in spatially extended systems that connect two different spatially homog...
Reaction–diffusion equations on the real line that contain a control parameter are investigated. Of ...
In this thesis methods from nonlinear dynamical systems, pattern formation and bifurcation theory, c...
Reaction–diffusion equations on the real line that contain a control parameter are investigated. Of ...
In this paper we show how to construct the Evans function for traveling wave solutions of integral n...
In this paper we show how to construct the Evans function for traveling wave solutions of integral n...
This is a study of fronts and patterns formed in reaction-diffusion systems. A doubly-diffusive vers...
This is a study of fronts and patterns formed in reaction-diffusion systems. A doubly-diffusive vers...
In this paper we show how a local inhomogeneous input can stabilize a stationary-pulse solution in a...
A stability analysis is presented for neural field equations in the presence of axonal delays and fo...
In this Letter we show that an inhomogeneous input can induce wave propagation failure in an excitat...
Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. ...
Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. ...
In this thesis methods from nonlinear dynamical systems, pattern formation and bifurcation theory, c...
Fronts are travelling waves in spatially extended systems that connect two different spatially homog...
Fronts are travelling waves in spatially extended systems that connect two different spatially homog...
Reaction–diffusion equations on the real line that contain a control parameter are investigated. Of ...
In this thesis methods from nonlinear dynamical systems, pattern formation and bifurcation theory, c...
Reaction–diffusion equations on the real line that contain a control parameter are investigated. Of ...
In this paper we show how to construct the Evans function for traveling wave solutions of integral n...
In this paper we show how to construct the Evans function for traveling wave solutions of integral n...
This is a study of fronts and patterns formed in reaction-diffusion systems. A doubly-diffusive vers...
This is a study of fronts and patterns formed in reaction-diffusion systems. A doubly-diffusive vers...
In this paper we show how a local inhomogeneous input can stabilize a stationary-pulse solution in a...
A stability analysis is presented for neural field equations in the presence of axonal delays and fo...
In this Letter we show that an inhomogeneous input can induce wave propagation failure in an excitat...
Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. ...
Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. ...