Exploring the frontiers of nonlinearity in Nature

Everything in our world is in motion. Mathematics can help us to understand these motions—and in some cases, even predict them. Take, for example, a wolf hunting in a forest: it preys on other animals for food, converting that energy into reproduction. If hunting is too intense, prey populations decline, eventually leading to a drop in the wolf population as well. This decline allows the prey to recover, restarting the cycle. These predator-prey dynamics often lead to natural population oscillations—something very simple nonlinear mathematical models can describe remarkably well. Such nonlinear dynamics are everywhere: in climate systems, lasers, viral infections, and ecosystems. Our research focuses on understanding these complex behaviors, especially in biological systems. We use tools from dynamical systems theory and statistical physics to explore how nonlinear processes evolve over time and how systems undergo transitions—what we call bifurcations—between different states.

Our work spans multiple areas within the biological sciences, unified by the theme of nonlinear dynamics. We collaborate with a broad and enthusiastic network of researchers in applied mathematics, systems and synthetic biology, theoretical ecology, and field biology. Together, we aim to uncover the principles governing dynamic behavior in life’s most complex systems.

“Scientists are perennially aware that it is best not to trust theory until it is confirmed by evidence. It is equally true . . . that it is best not to put too much faith in facts until they have been confirmed by theory.”

Robert MacArthur (Geographical Ecology, 1972)