The Indian Institute of Science Education and Research (IISER) Thiruvananthapuram, in association with prominent research institutions, have answered a question that has perplexed scientists for half a century – what makes large and complex networks stable?
The study was undertaken in collaboration with the International Institute of Information Technology (IIIT) Hyderabad, CNR – Institute of Complex Systems (ICS), Italy; and Bar-llan University, Israel. The research involving a mathematical framework is believed to have real-world implications in heterogenous networks – social, power, data and even genetic; infrastructure, the Internet and health-care ecosystems.
The research has been published in the peer-reviewed journal Nature Physics in a paper co-authored by Chandrakala Meena, assistant professor, School of Physics, IISER Thiruvananthapuram; Chittaranjan Hens, assistant professor, IIIT Hyderabad; Stefano Boccaletti of CNR – ICS; and the trio of Baruch Barzel, Simcha Haber and Suman Acharyya of Bar-llan University.
The international research team explored a concept put forth by theoretical physicist Robert M. May who studied the relationship between species diversity and stability in ecosystems around 50 years ago. He had employed mathematics to show that having more species made the ecosystem less stable. The new study found that May’s calculations did not account for the fact that some nodes (or species, in the case of the biodiversity problem) in large heterogeneous networks have many more links than others. These additional links that were neglected in May’s study add to the strength and resilience of the network, they claimed.
The scientists used Jacobian ensemble, a mathematical framework, to study the stability of complex systems. This approach uses matrices to describe various relationships inside a system and to understand how small changes can affect its behaviour over time. The researchers found that when a network is large and heterogeneous, it is better able to handle changes and is less sensitive to perturbations.
Explaining the significance of the work, Dr. Meena pointed out that the stability of systems is a complex problem. “If you change something small in the system, it could become unstable like trying to balance a pole on its end. But in our research, we discovered that even large and heterogeneous networks can be robust. It can continue to work as intended because of the additional links, even if you apply a lot of stress on the system or perturb things inside it. This explains why many natural or man-made heterogenous and large network systems, like our brains and the Internet, do not collapse even when many factors in the system change.”
