A Network That Rings Before the Lurch

Original: "Network percolation provides early warnings of abrupt changes in coupled oscillatory systems: An explanatory analysis"

· Noémie Ehstand, Reik V. Donner, Cristóbal López, Emilio Hernández-García

arXiv:2305.05450 · 2023-05-09 · CC BY 4.0 · 2 min

Statistical Mech Chaotic Dynamics Atmospheric and Oceanic Physics physics.data-an

Spatial correlations in a network of coupled oscillators give an early warning of an abrupt regime shift before the system jumps.

A fisherman pulls on his net and listens to it ring. Each strand quivers in its own way, but before a strong tug, all the strands begin to vibrate in unison. So it is with complex systems: before a sharp state jump, the individual parts suddenly start to oscillate in concert, and that synchrony betrays the coming jump.

Scientists built a model of 500 coupled FitzHugh–Nagumo oscillators arranged on a ring. These are mathematical pendulums that can abruptly flip the sign of a fast variable, like a neuron that suddenly fires. Between oscillators, they placed links whose strength depended on how synchronously the oscillators moved. The result is a network: nodes are points in space, and links are statistical dependencies between their oscillations.

The network is invisible to the eye, but you can feel it. If the connection between two nodes is stronger than a threshold, they count as linked. Then clusters form from individual nodes, and before a jump, the largest cluster begins to grow, like a crack in ice spreading before it breaks.

It turns out that the size of the largest cluster grows well before the jump and reaches its maximum at the moment of transition. Even earlier, a peak appears in the probability that a random node belongs to a cluster of size two. It is as if small groups of people in a square first pair up, then merge into a single crowd. Spatial variance does not provide such an early warning.

To understand what actually drives the rise in correlations, the researchers removed the slow trend from the data. If the precursor remains, then critical slowing down is at work: the system returns to equilibrium more and more slowly before the transition. If it disappears, the overall trend is to blame.

A test on real sea-surface temperature data from the NINO3.4 region showed that the peak in the probability of a size-two cluster precedes El Niño and La Niña by 79–214 days. But after detrending, the signal vanished. So in the ocean, the network rings not because of slowing local dynamics, but because of an overall large-scale temperature trend. The fisherman hears the net ring, but now he knows it can be caused by different things.

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The peak in the probability that a node belongs to a component of size two (c2) arises because small clusters first grow and then merge with the giant component, as if separate groups of people in a square first formed pairs and then merged into a single crowd.

\rho_{ab} = \frac{\sum_l p_a(t_l) p_b(t_l)}{\sqrt{\sum_l p_a(t_l)^2 \sum_l p_b(t_l)^2}}

A measure of linear association between deviations from the mean at two points

c_s = \frac{s n_s}{N}

Fraction of nodes that belong to clusters of size s

Concepts

Neural Network Oscillations mixed mode oscillations climate network El Niño equatorial wave propagation neural networks ERSST oscillation NOAA PMEL / TAO La Niña Teleconnection random fluctuation North Atlantic Oscillation recharge oscillator model fluctuation-dissipation theorem El Niño index spring predictability barrier synchronization autocorrelation function seasonal cycle

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A Network That Rings Before the Lurch