A viral video shows hundreds of thousands of starlings in flight, in no apparent formation but in such perfect coordination that no bird collides with another. This ‘murmuration’ evokes ceaseless amazement.
But is there some science behind such unspoken coordination? Scientists have attempted to decipher collective behaviour. ‘Herd mentality’ is the colloquial term, but ‘collective behaviour’ is undergirded by science. If you learn to model it, you can make use of it.
Indian Institute of Science Education and Research (IISER), Thiruvananthapuram, South China Normal University, Potsdam Institute for Climate Impact Research, and Humboldt University, Germany, have jointly met with some success in this area. They have proposed a new mathematical model for the emergence of the collective dynamics of any D-dimensional system in an effort to capture more accurately the real-world phenomena.
The functioning of the brain is a classic example of collective behaviour wherein functions emerge through the collective behaviour of many interconnected neurons.
Synchronisation in collective dynamics occurs due to coupling between individual elements. It is the adjustment of rhythms between the individuals participating in the collective behaviour and can occur in different spaces and time scales. An example of synchronisation in collective dynamics is the flashing of fireflies. Fireflies are known to synchronise their flashing patterns, which occurs due to the competitive flashing of male fireflies during courtship. The adjustment of rhythms between the fireflies allows them to produce a stunning display of synchronous flashing.
A paradigmatic mathematical model used to study collective behaviour is the ‘Kuramoto model’. This model explores synchronisation in large groups of interacting individuals, Dr Senthilkumar DV, Associate Professor, School of Physics, IISER, told Quantum. However, there are limitations as they do not take into account the amplitude dynamics, which is the intensity or strength of an individual’s behaviour. This drawback is evident in numerous real-world contexts, such as brain networks, where the strength of activity at one neuron can influence the response at another neuron or the receiving site.
Senthilkumar and his collaborators have proposed a new mathematical model that includes both ‘phase’ and ‘amplitude’ information. They believe it better captures the self-organisation of collective behaviours in diverse physical and biological systems.
“This high-dimensional phase-amplitude model includes the D-dimensional Kuramoto phase model as a special case in the weak coupling limit, which provides a broader perspective of the recent results of the D-dimensional Kuramoto phase-only models,” says Senthilkumar. Their proposed model can be used to study a wide range of systems, including magnetic colloids, active spinners, self-propelling systems, and swarming drones or insects. Their model works well for 3D realistic systems, making it useful in studying collective behaviour in nature.