Will a Large Complex System be Stable?


We can intuitively tell what makes a complex system with interacting components stable. For example in ecosystems, we know that the extinction of a prey species can lead to a mass extinction of predator species that feed on prey to sustain themselves, and genetic diversity helps organisms adapting to changing environments and rapidly evolving diseases. But is there a way to quantify stability with maths? When mathematicians speak about the stability of ecosystems, they usually refer to the asymptotic stability of an equilibrium point, characterised by the eigenvalues of a species interaction matrix. In reality, however, these interaction coefficients are difficult - if not impossible - to measure. Therefore in 1972, Robert M. May introduced a community matrix model, where coefficients are sampled from a random distribution, and derived a stability criterion based on the distribution of the eigenvalues using random matrix theory. For nearly 50 years, this model has been improved and applied in theoretical ecology.

Nov 26, 2020 10:15 AM
Bath Postgraduate Student Seminar