Spatially inhomogeneous two-cycles in ecological integrodifference equations
Bibliographic record
Abstract
In this thesis, we use the tools of computer-assisted proofs to demonstrate the existence of a period-two orbit in an infinite-dimensional discrete dynamical system that models dispersal population growth. In particular, the model combines the logistic/Ricker growth map together with a Laplace dispersal kernel. We reformulate the problem of looking for a period-two orbit into one of finding a connecting orbit between two fixed points in a four-dimensional ordinary differential equation. We solve this problem in two steps. First, we rigorously compute local stable and unstable manifolds attached to the two fixed points. Second, we rigorously solve a projected boundary value problem, with the boundary values being on the invariant manifolds. A key symmetry in the system allows us to solve for only half of the orbit, requiring computations only for the stable manifold of one fixed point. For both subproblems, we formulate an appropriate equivalent zero-finding problem on a Banach space of normed sequences. We obtain approximate solutions by projecting the zero-finding problems to finite-dimensional spaces and applying Newton's method on carefully selected initial conditions. Finally, we validate these solutions using a Newton-Kantorovich type theorem
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".