Exploring the frontiers of nonlinearity in complex systems

Everything in our world is in motion. Mathematics provides a powerful way to understand these motions (dynamics) and, in some cases, even predict them. Consider a wolf hunting in a forest. By preying on other animals, it acquires the energy needed to survive and reproduce. If predation becomes too intense, prey populations decline, eventually causing the wolf population to decrease as well. As predator numbers fall, prey populations recover, and the cycle begins again. These predator–prey interactions often generate natural population oscillations that can be captured remarkably well by simple nonlinear mathematical models.

Such nonlinear dynamics are not unique to ecosystems. They are ubiquitous in natural and artificial systems, appearing in climate systems, lasers, viral infections, neural activity, particle accelerators, and countless other complex phenomena. Understanding how these systems change over time is at the heart of our research. We use mathematical tools from dynamical systems theory, statistical physics, and computational biology to investigate how complex processes evolve and how they transition between different states through critical changes known as bifurcations.

Our research spans diverse areas of the life sciences, united by a common interest in nonlinear dynamics and complex systems. We work closely with a broad and enthusiastic network of collaborators in applied mathematics, systems and synthetic biology, theoretical ecology, virology, and field biology. Together, we seek to uncover the fundamental principles that govern the dynamic behavior, resilience, and evolution of living systems across scales.

“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)