Research Projects

Collective dynamical patterns are common in nature, ranging from physics, biology, and neuroscience to engineering and social-economic systems. Multifaceted progress in understanding the evolutionary aspects of studying collective dynamical states in the coupled oscillator's various coupling and nonlinear forces has led to many new concepts and ideas during the last few decades. Hence, understanding complex networks and the emergence of their collective behaviour becomes inevitable to understand the systems around us to manipulate and control them for beneficial outcomes. During the past decades, collective synchronization patterns have been considered essential in many real-world networks. However, a combination of synchronization and swarming recently occurs in diverse contexts, from biological micro-scale collectives and chemical micromotors to magnetic domain walls and robotic drones. Despite being commonplace, this interaction between synchronizations and swarming must theoretically be better understood. In general, oscillators that can synchronize in time but not space have been the focus of the synchronization study. The opposite has been done in swarming research, which has looked at units that move through space and synchronize spatially based variables like orientation but not internal phase variables in time. As a result, the interaction between synchronization and swarming specifies a novel class of collective dynamics that are still largely unexplored. Recently, the investigation of various collective dynamical patterns in coupled oscillators and swarmlators has been an active area of research. However, the effect of noise, feedback, external stimuli/event, delay coupling, symmetry-breaking interaction, the robustness of higher-order interaction, and force is still in its beginning and not well studied in the literature. It requires more attention to understand more realistic dynamics in the many phenomena and their applications in coupled oscillators and the population of swarming coupled oscillators. These facts contribute to the motivation behind this proposal. In this project, we planned to develop a deep and rigorous understanding of a broad class of coupled oscillators and swarmalators' complex dynamical systems with external stimuli, generically represented by a homogeneous and heterogeneous network of interconnected oscillators. Our findings will enrich the current study of swarmalators and coupled oscillators, emphasizing many competitive interactions in the swarmalator systems. We also envisage many possibilities for application to swarmalators in robotics (swarmalatorbots) and magnetic domain walls. Further, in recent times collective dynamical states in complex systems continue to bring in novel features that can explain many natural phenomena and lead to many new applications. Therefore, we can expect rich dividends from our studies shortly.