Posts Tagged ‘complex social systems’

Phase transitions in network ecosystems

Tuesday, May 4th, 2010 by Antonio Manzalini


Phase transitions occur in a system when a small change in some parameter leads to a dramatic change of some characteristic property of the system. An order parameter is some observable physical quantity that is able to distinguish between two distinct phases.


A well known physical example is a magnet which exhibits magnetism up to a critical temperature, above which its magnetic properties are suddenly destroyed. In the same way, when cooling a material, such as iron, the spins of individual atoms will organise themselves spontaneously into alignment below the critical temperature and the material becomes magnetic. Landau symmetry breaking theory provides a deep insight into phase transitions: for example it points out that hat different phases have different symmetries and that phase transition is simply a transition that changes the symmetry.


Amazingly study and analysis of phase transitions is an active research topic not only in Physics but also in Computer science and even in social complex systems; please have a look at these slides:


Concerning communication networks, for instance, they showed [1] the presence of a phase transition in network traffic, separating the low-traffic phase (with no congestion) from the congestion phase, as the packet creation rate increases. Phase transition point depends on how each node chooses a path for the packets; in particular, they demonstrated that an appropriate randomness in path selection can shift the onset of traffic congestion to accommodate more packets in the model network.


It easy to imagine that if the terminals will play the role of intelligent connecting nodes future network environments will be such pervasive and complex that different forms of phase transitions may happen. Consider not only Users’ behaviours, but also that terminals and nodes will include several interacting control-loops for self-management purposes. Nature teaches us that these control loops can be combined in emergent algorithms in several ways [2]: for instance, in the termites algorithm when the threshold of one control loop has been met, then the algorithm changes state to use another control loop responding to a different threshold; in the flocking and moth algorithms the meeting of one threshold then leads to another threshold. These combinations determine emergence of complex social behaviours.


On the other hand, even if all (self-management) control loops will be made explicit and the operating regions will be well-defined, interactions between said control loops can result in complex behaviours difficult to understand and predict[3]. So, phase transitions may occur putting at risk even the stability of the whole network, and jeopardizing the local or global performances. On the other hand, controlling the equivalent order parameters of the network might be a useful mean to achieve higher performance and survivability. The problem is identifying such order parameters.



  1. T.Ohira and R.Sawatari,”Phase transition in computer network traffic model”, Physical Review E, vol. 58, pp. 193-195 (1998)