A *nonlinear* relationship between two variables is one where an incremental change in one leads to a nonproportional change in the other variable. Instead, a small change in one variable, at the right place and time, can produce a large effect at some other place and time, or vice versa. These nonlinear relationships are the hallmark of *d ynamical *systems: those whose properties or behaviors change over time or space. Living systems are typical examples of dynamical systems with many interrelated parts or subsystems, from small-scale cellular relationships to large-scale population relationships. The behaviour of one subsystem, with its own dynamics, becomes the input for another subsystem, imposing certain constraints on its dynamics. This is how coupled

*nonlinear dynamics,*or Complex Dynamics, arise. Mathematics, physics, and life sciences have contributed important theoretical developments to the understanding of how nonlinear dynamics can explain behaviour in a wide range of disciplines in life sciences and social sciences, based on common principles arising from differential equations. These models address how complex systems are formed, how they evolve, and how they can break down. The Complex Dynamics training grant builds on foundational themes and applies them in three topic areas (see “themes” for more details).