Spatiotemporal Dynamics of Competing Species With or Without Memory Under Dirichlet Boundary Condition
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Bibliographic record
Abstract
ABSTRACT We investigate a diffusive Lotka–Volterra competition model with temporally distributed memory and Dirichlet boundary conditions, focusing on the interaction between a species with memory and one without. The memory‐capable species exhibits both self‐memory and cross‐memory, while the memoryless species relies solely on random diffusion. We analyze the existence and stability of steady‐state solutions, including semi‐trivial and positive steady states, under two distinct memory kernel cases. In the weak kernel case, where memory fades over time after immediate acquisition, the positive steady‐state solution remains locally asymptotically stable for all non‐negative delays. In the strong kernel case, where memory follows both an acquisition and decay phase, Hopf bifurcations arise as delay increases, leading to instability and the emergence of nonhomogeneous periodic solutions. Our findings reveal that species with self‐memory gain a competitive advantage, increasing their likelihood of survival, while those relying solely on cross‐memory face a higher risk of extinction. This contrast underscores the crucial role of different memory types in shaping competitive outcomes.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it