Understanding the relationship between complexity and stability in large dynamical systems - such as ecosystems - remains a key open question in complexity theory which has inspired a rich body of work developed over more than fifty years. The vast majority of this theory addresses asymptotic linear stability around equilibrium points, but the idea of `stability' in fact has other uses in the empirical ecological literature. The important notion of temporal stability describes the character of fluctuations in population dynamics, driven by intrinsic or extrinsic noise. Here we apply tools from random matrix theory to the problem of temporal stability, deriving analytical predictions for the fluctuation spectra of complex ecological networks. Excitingly, we are able to show how different network structures leave distinct signatures in the spectrum of fluctuations, opening the door to a new avenue of research in the age-old complexity/stability debate .
Understanding the relationship between complexity and stability in large dynamical systems -- such as ecosystems -- remains a key open question in complexity theory which has inspired a rich body of work developed over more than fifty years. The vast majority of this theory addresses asymptotic linear stability around equilibrium points, but the idea of `stability' in fact has other uses in the empirical ecological literature. The important notion of `temporal stability' describes the character of fluctuations in population dynamics, driven by intrinsic or extrinsic noise. Here we apply tools from random matrix theory to the problem of temporal stability, deriving analytical predictions for the fluctuation spectra of complex ecological networks. We show that different network structures leave distinct signatures in the spectrum of fluctuations, and demonstrate the application of our theory to the analysis ecological timeseries data of plankton abundances .
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temporal stability
`temporal stability'
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Excitingly, we are able to show how
We show that
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opening the door to a new avenue of research in the age-old complexity/stability debate
and demonstrate the application of our theory to the analysis ecological timeseries data of plankton abundances