Stability of travelling waves in stochastic Nagumo equations

Tuesday, October 23, 2012 - 2:00pm - 2:50pm
Keller 3-180
Wilhelm Stannat (TU Berlin)
Stability of travelling waves for the Nagumo equation on the whole line is proven using a new approach via functional inequalities and an implicitely defined phase adaption. The approach can be carried over to obtain pathwise stability of travelling wave solutions in the case of the stochastic Nagumo equation as well. The noise term considered is of multiplicative type with variance proportional
to the distance of the solution to the orbit of the travelling wave solutions.

The motivation for our study is to understand the stability properties of the action potential travelling along the nerve axon under the influence of thermal noise, that can be modelled in a mathematical idealized way with the help of stochastic FitzHugh Nagumo systems. In our talk we will demonstrate how the stochastic stability for the action potential leads to a simple computational approach for estimate the probability of propagation failure in nerve axons.
MSC Code: