Martin Wechselberger

Professor of Applied Mathematics, University of Sydney

I am an applied mathematician with expertise in the fields of dynamical systems and, in particular, geometric singular perturbation theory. My research focuses on developing rigorous analytical and geometric tools to understand complex rhythms, patterns and threshold phenomena in multi-(time)scale systems, with applications in mathematical physiology, ecology and other sciences.

In 2017, I was awarded the J.D. Crawford Prize “for breakthrough insights, highlighting the importance of canards and mixed-mode oscillations (MMOs), that have applications to neuroscience and open up new fields of research for dynamical systems with multiple time-scales.”

Research Focus

My work addresses the challenge of analysing multiple timescale problems “beyond the standard form” where traditional splitting techniques fail. Current research highlights include:

• Geometric Singular Perturbation Theory: Advancing coordinate-independent methods and higher-order averaging to resolve hidden timescale structures.
• Canard Theory: Proving the existence and bifurcation of exceptional solutions that shape transient dynamics in arbitrary dimensions.
• Rate-Induced Tipping (R-tipping): Developing a novel geometric framework to predict “tipping points” in systems subject to environmental change, such as ecosystem collapses and climate events.
• Mathematical Physiology: Providing widely accepted explanations for complex oscillatory patterns and threshold phenomena in neural and neuroendocrine models.

Academic Leadership

I am part of the Sydney Dynamics Group (SDG) and serve as a Professor in the School of Mathematics and Statistics at the University of Sydney. My research program has been consistently supported by the Australian Research Council (ARC), including a prestigious Future Fellowship and multiple Discovery Projects.

I maintain a global collaborative network, including frequent partnerships with researchers in the USA, EU, and New Zealand.