| Abstract: |
| Autocatalysis is a fundamental mechanism for self-amplification and positive feedback in reaction networks. Using a structural (i.e., network-based) definition, autocatalysis provides a sufficient condition for a network to admit an unstable equilibrium. More specifically, a Perron-Frobenius argument links autocatalysis to a possible positive growth of the system. Albeit with different wording, bifurcations in epidemiological networks are most naturally a consequence of autocatalysis too (see e.g. works by Adenane and Avram, also participating in this special session). In this talk I will overview such ideas and present examples of reaction networks where multistationarity (including co-existence of stable equilibria) and periodic oscillations are triggered by autocatalysis. I will also discuss how autocatalysis is a natural, but not exhaustive, route to instability, and show examples where non-autocatalytic forms of instability arise. |
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