The role of distributed time delays in the dynamical behaviour of coupled systems...
Channel: Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC)
Date: 2017-03-29

- By: Yuliya Kyrychko
- Affiliation: University of Sussex
- Date: 2017-03-29T14:30:00+00:00

 In the last decade, the use of coupled systems, such as global peer-to-peer social networks, ad
hoc mobile networks and neural networks, has become more and more prevalent. These networks
are highly dynamic in nature, with quickly evolving topologies. One of the fascinating properties of such networks is that their emergent behaviour can be complex yet often self-organised. 

In this talk I will present Hopfield-type neural network models, where one sub-system receives a delayed input from another subsystem. The model includes a combination of both discrete and distributed delays, where distributed time delays represent the
neural feedback between the two sub-systems, and discrete delays
describe the neural interactions within each of the two subsystems.
Stability properties are investigated for different commonly
used distribution kernels, and the results are compared to
the corresponding results on stability analysis for networks with
no distributed delays. I will show how boundaries of the stability
region of the trivial equilibrium can be obtained analytically for
the cases of delta, uniform and gamma distributions. Direct numerical
simulations that confirm analytical findings will also be
presented.