Effects of spatiotemporal, temporal and spatial nonlocal prey competitions on population distributions for a prey-predator system with generalist predation
Why this work is in the frame
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Bibliographic record
Abstract
Conventional wisdom suggests that a prey-predator system with a generalist predator exhibits more stable dynamics than with a specialist predator. However, recent developments show that the presence of a generalist predator can lead to comparatively complex dynamics, including bistability, tristability, and several local as well as global bifurcations. In this paper, we study the dynamics of both local and nonlocal models of prey-predator interactions with generalist-type predation. Nonlocal intra-specific prey competition is assumed to be spatiotemporal, purely temporal, or purely spatial in nature. Also, we primarily aim to understand the resulting system dynamics under conditions of subpar and limited substitute food options available to the generalist predator. We first ensure that the local model is well-posed, and then provide the conditions for the existence and non-existence of spatially heterogeneous steady state solutions by using the maximum principle, Poincaré inequality and Leray-Schauder degree theory. Further, we derive the conditions for Turing instability in both the local and nonlocal models by using the linear analysis. We then illustrate a wide class of stationary and dynamic patterns obtained through numerical simulations for all the considered models, where the choice of the parametric domain is partially guided by the analytical results. This study reveals that the nonlocal model with purely spatial kernel admits spatial-Hopf bifurcation which gives rise to population oscillations around a 'ghost attractor', whereas this phenomenon does not occur in the other models.
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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 | 0.000 | 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 | 0.000 |
| 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