Investigating the dynamical behaviour of complex systems such as the human brain, the weather, etc. is of great importance in modern nonlinear science and has gained attention in various fields such as physics, chemistry, biology, and engineering. The traditional reductionist approaches used in science and engineering are not suitable for investigating these systems, and one needs to use the theories of network science to mathematically model the complex interacting effects of the large number of units in these systems. In the context of dynamics of such complex networked systems, the most prominent phenomena that play an important role in characterizing their dynamical behaviour include synchronization and suppression. Synchronization refers to the phenomenon when all the dynamical units, randomly connected, start behaving in coherence as a single unit. This is essentially a phase transition and occurs only in regimes where the system parameters are conducive for such a phenomena. These transitions have importance in the context of applications that include neuroscience, climate or even in energy harvesting from ambient vibrations and can be beneficial in some cases (such as in energy harvesting) and deleterious in others (as in neuroscience). Identification of the route of these transition regimes is therefore important and is investigated by varying the system parameters. The route to synchronization could be gradual or abrupt with the latter being referred to as explosive synchronization (ES). On the opposite end of the spectrum, the suppression of the dynamics is referred to as amplitude death (AD) and can be gradual or explosive. Amplitude death is observed in lasers and neural systems and in biological systems such as, in cell differentiation. Explosive death happens when a network of coupled oscillators transition from oscillatory state to a synchronized state of no oscillations.
The aim of the recently published study, conducted by Ms. Samana Pranesh and Prof. Sayan Gupta from The Uncertainty Lab, Department of Applied Mechanics, Indian Institute of Technology (IIT) Madras, Chennai, India (Prof. Sayan Gupta is also from Complex Systems and Dynamics Group, Indian Institute of Technology (IIT) Madras, Chennai, India), was to investigate analytically, under general settings, the mechanisms which lead to explosive death transitions in a mean field coupled complex network of oscillators. The study found that explosive death transitions are characterized by hysteresis on adiabatic change of the important system (bifurcation) parameter and developed analytical conditions for these hysteresis points, thereby identifying the parameter regimes of concern. The theoretical developments were validated through numerical examples, involving networks of limit cycle systems and for chaotic systems. The results from this study provide insights into the selection of parameters while designing complex dynamical systems, so that first order transitions – which are abrupt and can lead to abrupt loss of functionality – can be avoided. These studies can be useful as well in assessing the robustness of existing systems against first order transitions.
Article by Akshay Anantharaman
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