# Asymptotic behaviour of a neural field lattice model with a Heaviside operator

Monday, June 4, 2018 - 11:00am - 11:50am

Lind 305

Peter Kloeden (Johann Wolfgang Goethe-Universität Frankfurt)

Motivated by the importance of discrete structures of neuron networks, a neural lattice system arising from the discretization of neural field models in the form of integro-differential equations is studied. The neural field lattice system is first formulated as a differential inclusion on a weighted space of infinite sequences, due to the switching effects, for which the usual existence theorems do not hold.

Then the existence of solutions of the resulting differential inclusion is proved by a series of sequential finite-dimensional approximations. This method of proof is particularly useful when delays and random terms are included in the model.

The solutions are shown to generate a nonautonomous set-valued dynamical system which possesses a pullback attractor. Forward omega limit sets for the set-valued dynamical system are also discussed.

The method of proof is also useful in ecological models where Heaviside switching terms are now being used.

Joint work with Xiaoying Han, Xiaoli Wang and Meihua Yang

Then the existence of solutions of the resulting differential inclusion is proved by a series of sequential finite-dimensional approximations. This method of proof is particularly useful when delays and random terms are included in the model.

The solutions are shown to generate a nonautonomous set-valued dynamical system which possesses a pullback attractor. Forward omega limit sets for the set-valued dynamical system are also discussed.

The method of proof is also useful in ecological models where Heaviside switching terms are now being used.

Joint work with Xiaoying Han, Xiaoli Wang and Meihua Yang

MSC Code:

34D45, 34G25, 37L60, 92D20