Complex systems. Rocket engines, cyclones, gas turbines, stock markets and epidemiology are all complex systems. And all complex systems have one fundamental characteristic: one small change in the initial variables and the system can behave in wildly different ways. Other characteristics include nonlinearity, emergence, spontaneous order, adaptation and feedback loops, among others.

The nature of complex systems makes them multi-disciplinary and specifically, Multi-physics, multi-scale and multi-layered. For example, in a climate system, we have multiple layers such as land, ocean and atmospheric systems that interact with each other.

It is in the nature of complex systems to undergo critical transition. During such critical transitions, the system shifts from one state to another for a slight change in control parameter. For example, a slight change in climate—and CO2 levels in the ocean—lead to destroyed coral reef ecosystems in the oceans. Nature unleashes fury through critical transitions in extreme weather and climate events.

Such critical transitions occur not only in obvious and visible scale in a large system like a climate system, but also in machinery, particularly in thermo-fluid machinery like rocket engines, jet engines and gas turbines. Thermoacoustic instability can lead to catastrophic failures in such machinery.

The Indian Institute of Technology Madras (IIT Madras) has established a research centre—with funding from the ‘Institute of Eminence’ initiative of the Government of India—to develop tools and techniques that detect and predict critical transitions, called ‘Critical Transitions in Complex Systems (CTCS) Centre of Excellence (CoE)’.

Enriched with researchers from engineering as well as natural sciences, the centre aims to study the emergence of spatial and temporal ordered patterns that can prove to be catastrophic.

Some of the focus areas of the centre include: Predicting and controlling instabilities (large-amplitude oscillations) in turbulent thermo-fluid and thermoacoustic systems such as those in combustors of rocket and gas-turbine engines; Studying and forewarning active-break phases of monsoon and extreme weather phenomena such as intense synchronised rainfall, which can cause flooding; Understanding and developing tools for predicting the occurrence of cyclones and super cyclones and merging of multiple cyclonic systems; and, Investigating the formation and the microphysical dynamics of clouds to understand the onset of precipitation and extreme weather events such as cloud bursts.

One might wonder how the focus areas of the centre will be approached given the vastly different areas of application. Therein lies the uniqueness in approach — that of critical transitions in complex systems.

For example, Covid-19 transmission and flame blowout in combustors are two unrelated phenomena; however, a research team (Indhuja Pavithran and Prof RI Sujith, IIT Madras) unravelled the striking similarities between the two. They identified the presence of a hyper exponential growth decorated with log-periodic oscillations preceding flame blowout and during the early phase of extreme Covid-19 waves.

In both cases, hyper exponential growth without a limit can cause problems.

Flame blowout (jet engines) in real-world systems, as well as diseases that spread quickly such as the Covid-19, are undesirable. Contrary to the commonly believed exponential growth, the faster-than exponential growth phase is hazardous and would need stricter regulations to be controlled. By studying the characteristics of these log-periodic oscillations, we can better predict the finite-time singularity in both cases.

Many complex systems transition towards a critical point following cascading events, and this process has a hierarchical structure that results in log-periodic oscillations. For instance, the accelerating occurrence of financial bubbles often ends in large market crashes and many smaller earthquakes presage larger earthquakes. Even though these are different systems, there is a striking similarity in their behaviour near the critical point among complex systems that are otherwise quite different in nature.

While the examples in this article are about disparate concepts like Covid spread and climate systems, there are practical applications in developing early warning systems. As Prof Sujith says, he is “focussed on the CoE’s contribution to energy security, national security, space exploration and early warning systems for natural disasters and extreme events.