The researcher from the Centre for the Study of Complex Systems of the Institute of Physics Belgrade, Dr Igor Franović published a mini-review paper on the regime switching in complex systems in the December issue of the Chaos journal. In addition to Dr I. Franović, the paper is authored by Dr Sebastian Eydam from the RIKEN Center for Brain Science in Japan and Dr Deniz Eroglu from Kadir Has University in Turkey.
According to Dr Franović, regime switching includes a qualitative change in the dynamics of complex systems due to a change in the conditions they operate on. ‘The change can occur due to one or several simultaneous actions of several factors,’ said Dr Franović supporting the statement with an example of climate models which frequently encompass a quick switching of parameters and noise.
The term regime switching is not limited to sudden and irreversible transitions, but it also includes gradual reversible processes. It also does not include individual isolated events but sequential activity patterns, stated Dr Franović giving examples of concepts observed in ecological and climate systems as well as in theoretical neuroscience.
The phenomenon of regime switching has been attracting attention due to multiple possibilities of applications, and the research is conducted on two levels. ‘One level is the advancement in mathematical methods, i.e. exact reduction methods, while the second level understands data-driven methodologies’ explains Dr Franović. When it comes to the second level, Dr Franović points out that recently there has been a breakthrough in model-free predictions of critical transitions to methods of deep learning. ‘Previous methods were often limited by the very class of the phenomenon or the class of the system which led to methods being adapted for example to synchronization phenomena or certain climate phenomena. In the last two years, techniques which allow the universality of application and robustness to some noise types have emerged,’ says Dr Franović.
As the paper alleges, one of the goals of complex systems control is the stabilization of their dynamics. ‘Stabilization of the dynamics most frequently includes the suppression of unwanted transitions inducted by noise which is unavoidable in complex systems and the elimination of co-existant metastable states that a system can transition to,’ Dr Franović explains mentioning that a significant advancement has been achieved in the last ten years in the development of new approaches for complex systems control. ‘The main challenge in the future is the development of new methodologies of sequential dynamics control, particularly various cyclic patterns (regular and chaotic) in applications to reservoir and neuromorphic computing.
Sometimes systems spend a long time in the vicinity of regime switching, for -example ‘at the edge of chaos’ where regular dynamics transition into chaotic behaviour. According to Dr Franović, there are scenarios where maintaining dynamics near this transition is desirable for achieving the system’s optimal functionality, and this can be achieved in various ways. ‘The concept of sustaining a state ‘at the edge of chaos’ is often discussed in the context of specific cortical brain regions, but also in connection with genetic regulatory networks, recurrent neural networks, cellular automata and reservoir computing,’ says Dr Franović, adding that the proven advantages of such states relate to the optimization of certain functions. ‘Dynamics can be regulated at this transition boundary through external influences, but it is also possible for the system to spontaneously maintain such a state, which is called the phenomenon of self-organized criticality,’ concludes Dr Franović.