Which System Variables Carry Robust Early Signs of Upcoming Phase Transition? An Ecological Example.

Which System Variables Carry Robust Early Signs of Upcoming Phase Transition? An Ecological Example.

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Growth of critical fluctuations prior to catastrophic state transition is generally regarded as a universal phenomenon, providing a valuable early warning signal in dynamical systems.Using an ecological fisheries model of three populations (juvenile prey J, adult prey A and predator P), a recent study has reported silent Counter Height Table early warning signals obtained from P and A populations prior to saddle-node (SN) bifurcation, and thus concluded that early warning signals are not universal.By performing a full eigenvalue analysis of the same system we demonstrate that while J and P populations undergo SN bifurcation, A does not jump to a new state, so it is not expected to carry early warning signs.In contrast with the previous study, we capture a significant increase in the noise-induced fluctuations in the P population, but only on close approach to the bifurcation point; it is not clear why the Grooming Brushes P variance initially shows a decaying trend.

Here we resolve this puzzle using observability measures from control theory.By computing the observability coefficient for the system from the recordings of each population considered one at a time, we are able to quantify their ability to describe changing internal dynamics.We demonstrate that precursor fluctuations are best observed using only the J variable, and also P variable if close to transition.Using observability analysis we are able to describe why a poorly observable variable (P) has poor forecasting capabilities although a full eigenvalue analysis shows that this variable undergoes a bifurcation.

We conclude that observability analysis provides complementary information to identify the variables carrying early-warning signs about impending state transition.