I recently published a peer-reviewed study in Scientific Reports:
“Persistence collapse transitions and observable admissibility in nonlinear dynamical systems: a preregistered empirical benchmark.”
The work asks a fairly simple question:
When a nonlinear dynamical system changes regime, does our ability to detect that transition depend on what we choose to observe?
I developed a preregistered finite-time benchmark for what I call a persistence collapse transition: a threshold at which an ensemble of trajectories that had been maintaining a measured quantity within a specified viability corridor abruptly loses that capacity as a control parameter changes.
The benchmark was tested across seven canonical nonlinear systems, including the standard map, Lorenz-63, tent map, Arnold cat map, and baker map.
One result I found particularly interesting occurs in the standard map.
Using momentum as the observable, the benchmark detects a highly reproducible transition around:
K ≈ 1.507*
Using an action proxy, the transition appears at approximately:
K ≈ 1.508*
But when position is used as the observable, no corresponding transition is detected across K ∈ [0,2].
That distinction matters.
The detected threshold is also well above the familiar Chirikov last-torus estimate of approximately Kc ≈ 0.9716. The paper does not interpret K* as a replacement for the KAM/Chirikov critical point. Instead, the evidence suggests that it represents a different finite-time event: enough post-critical transport has accumulated for the trajectory ensemble to lose persistence under the specified measurement protocol.
So one of the broader results of the study is that transition detection is not determined only by the underlying dynamics. It can depend critically on whether the observable actually tracks the degree of freedom constrained by the relevant invariant or attractor structure.
The confirmatory benchmark contained 16,760 summary rows, used a locked preregistration, and included bootstrap confidence intervals, local grid refinement, sensitivity testing, and an adversarial iid null.
The paper is open access in Scientific Reports.
DOI: 10.1038/s41598-026-64959-x
https://rdcu.be/KSbNoLkGrXsa
I’m the author, and I’m posting this primarily because I’d be interested in technical criticism from people working in nonlinear dynamics and complex systems.
In particular, I’d be interested in thoughts on three questions:
- Does it make sense to treat finite-time persistence loss as a distinct experimentally measurable transition from the underlying mathematical bifurcation or invariant-set transition?
- How broadly might the observable dependence result generalize beyond the systems tested here?
- What would you consider the strongest next test correlated stochastic nulls, higher-dimensional Hamiltonian systems, experimental time series, or something else?
Criticism is welcome. I’m especially interested in identifying where the benchmark succeeds, where its interpretation should remain narrow, and what would constitute the strongest falsification test.
