Leírás
The ODE model of a network of $n$ identical units (e.g. neurons) is studied. Each unit has its own differential equation and their behaviour is joined by the adjacency matrix of the network, leading to a system of $n$ non-linear ODEs. The Hopfield model of a neural network is an example for this complex system. The structure of the network has a strong effect on the dynamical behaviour of the system that has been widely studied. We show three classes of networks when suitable Liapunov functions guarantee the global stability of a unique steady state. In our study the weight matrix of the network is assumed to have a special structure. Namely, it is assumed that the edges starting from a neuron have the same weight. This enables us to determine the bifurcation diagram analytically when we have identical excitatory neurons and a few inhibitory neurons. In the well-known case of excitatory neurons only, there is saddle-node bifurcation. When a single inhibitory neuron is also present, then Hopf bifurcation may also occur and can be determined analytically. Adding more inhibitory neurons we show numerically that the bifurcation diagram becomes significantly more complex giving rise to appearing periodic orbits and multi-stability.
Zoom link: https://zoom.us/j/93746696898?pwd=b1J2MnEwMVdDVElPUFRkYWdtVXdWdz09
Meeting ID: 937 4669 6898
Passcode: 280561