Research Projects

Complex networks are ubiquitous in nature and technology, providing a framework for understanding the dynamics of interconnected systems. While most earlier studies have focused on static networks, adaptive dynamical networks (ADNs) are an emerging paradigm in the study of complex systems, which are characterized by the co-evolution of network structure and the dynamics of the nodes.  ADNs realistically capture the  dynamics of many real-work systems  where bidirectional feedback between node dynamics and network topology plays a crucial role. Some prominent examples include  the brain, social networks, and power grids. Recent studies have revealed intriguing phenomena in ADNs like hierarchical frequency multiclusters, recurrent synchronization, solitary states, and heterogeneous nucleation in ADNs, highlighting the intricate interplay between adaptation mechanisms and collective dynamics. The research in ADNs is still in its  preliminary stage, leaving many aspects of adaptive networks unexplored. This proposal aims to bridge research gaps with the most relevant and impactful problems. These problems include the investigation of heterogeneous nucleation phenomena in ADNs with higher-order interactions, as well as the collective dynamics of adaptive multiplex networks with structural correlations such as degree correlation and link overlap. Additionally, the project will  also explore  dynamics of resource-constrained adaptive networks. The research will employ a combination of numerical simulations, and analytical techniques such as dimensionality reduction techniques or mean-field approach for the deeper insights. The outcomes of this research are expected to advance the theoretical understanding of ADNs and provide new insights relevant to neuroscience, epidemiology, social, and engineered systems.