The mathematical laws of life manifest scaling regularities such as the relationship between mass and metabolism for the smallest to the largest organisms on Earth. These laws lack essential components representing interaction between organisms while sharing limited resources. Once accounted for, these components can bring significant variation to the predicted demographic laws using just metabolic scaling theory and can give mathematical descriptions for observed ecological phenomena. The oscillations in population number, where spikes in the number of organisms of a specific size propagate from small to large organisms is an example of such a phenomena. Here, we incorporate spatial competition and resource variation in a differential equation model for the population dynamics of sessile organisms. We use analytic and numerical tools to solve the corresponding equations and to characterize the form of instabilities that generate the oscillations, which we use to identify hidden mechanisms that may drive instabilities in ecological systems such as forests. As a result, we may be able to identify the most significant factors that affect the stability of an ecosystem corresponding to resource fluctuations that may become more prominent with climate change.
Niraj Kushwaha has a masters in physics from the Indian Institute of Technology Indore. His master’s thesis was in the field of non-linear dynamics and complex networks.
For his masters’ thesis, Niraj performed network modeling using Kuramoto’s oscillators to study collective behavior found in many real-world systems and also studied critical transitions between synchronization and chimera(solitary) states found in dynamical networked systems. In order to study the phase space of such systems, he used a unique technique that used machine learning to draw boundaries between the different phases.
Niraj’s research interest lies at the intersection of statistical physics, collective behavior, network science, computational modeling, data analysis and machine learning. Through his research, he wishes to study the hidden universal laws of nature, using various tools and techniques that fall under the umbrella of complexity science.
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Niraj Kushwaha will give a talk on Friday, March 17, 2023 at 3 PM in Room 201.