High-dimensional dynamical systems are ubiquitous in nature. They typically involve thousands to millions of state variables, depending on the type of system under question, which is required to describe the state of the system. Studies of dynamical systems spanning the last few decades have focused mostly on the simpler systems involving few state variables or approximate low-dimensional models describing the underlying high-dimensional system. In recent years, the emergence of sophisticated analytical and computational tools has allowed us to
study these systems in much finer detail. Examples of such systems range from brain structures, climate models, epidemiological models, population models, and so on. While these studies are motivated by various interdisciplinary areas, they can be mathematically described using difference, ordinary-differential or partial-differential equations in one or more dimensions. The interactions between different dynamical components in such models can be described using a complex network structure having pairwise or even higher-order interactions.
These lead to the observation of interesting phenomena like synchronization, explosive transitions, chimeras, and so on.

In this talk, I will present our results from multiple studies which aim to
investigate the dynamics of high-dimensional dynamical systems from both: a fundamental perspective, where we aim to characterize the fundamental properties of a system (like Lyapunov exponents) and how they scale with the dimension of a system; and also from an emergent-phenomena perspective where we study the occurrence of phenomena like synchronization (in a multi-layer network) and explosive transitions (in a neuronal network). I will also outline our simulation strategy which allows us to rapidly run simulations for such large systems and end with future plans for our work.