IISER MOHALI

Abstract: The study of nonlinear dynamics and pattern formation theory provides a powerful lens through which to explore the behaviour of complex systems across diverse scientific and engineering disciplines. Nonlinear interactions give rise to a wide range of phenomena, such as chaos, self-organization, and various patterns. I will discuss the theoretical underpinnings of nonlinear dynamics and pattern formation, focusing on their mathematical modelling and real-world applications. The key topics include the various types of emergent collective dynamical states in complex dynamical networks, the resilience of the networks, and the role of symmetry-breaking in emergent behaviours. As a case study, I will discuss the vegetation pattern formation phenomenon in resource-limited environments in response to climate change. I will discuss the underlying driving mechanism of spatial self-organizing patterns and the various community properties. I will discuss the eco-evolutionary dynamics and the ecosystem's response and propose mitigation strategies to alleviate environmental stress, aiming to maintain robust ecosystem functions and stability in response to climate extremes.