It turns out that the model we consider is very sensitive to parameters, i.e., a slight change in a parameter, e.g. a diffusion constant, can prevent bundling, debundling or attachment. The parameter values for which bundling, debundling and attachment occur are however within ranges corresponding with experimental measurements. At the cellular level the signaling between neurons is highly nonlinear due to the complex interactions between neurotransmitters, receptors, second messengers and ion channels that are involved. The model is an extended Hodgkin-Huxley type model partly based on experimental data and is analysed with the use of nonlinear system analyses, phase space analyses and bifurcation theory. Although the details of this phenomenon depends on the type or synapse and the brain area, a common trend is that synaptic strenght decreases as a result of presynaptic activity with a characteristic time scale of about 10 msec.
Recovery occurs in the order of seconds.
These synaptic mechanisms can have quite profound functional consequences on the behaviour of neural networks. For instance, attractors in recurrent neural networks will become metastable states due to the changing connectivity pattern. In this presentation I will present both numerical and analytical results of this new phenomenon. Recently, the neuroscientists D.R. Chialvo and P. Bak of the Divison of Neural Systems in Copenhagen suggested a hormone controlled way to adapt the synapses. This control mechanism might be realized by an actual brain to adapt itself in such a way that it can perform the desired input-output relations.