Development of complex networks based on memory properties of biological switches

Network theory is a successful set of methods used in the complex system analysis and description. While the topological structure and the dynamical consequences of this approach is well known, the theory of network generation is still lacking a well rounded set of methods and theorems, except for a small set of models. Most models have boolean and iterative structure, based on the Erdos-Renyi, Barabasi-Alberts or Watts-Strogatz models. We present a differential equation model based on the bistability and hysteresis properties of neural plasticity as described by the BCM model, that we have extended from single neuron to a whole network. This model is capable to generate interesting network topology starting from a three neuron-based, non-local parameters, which describe the interaction between incoming and outgoing links from each neuron. The underlying concept of the model is the idea of symmetric competition or collaboration between individual link. The resulting system shows convergent solutions and non-trivial behaviours for a great range of parameters.