延迟放置决定基于污染的旅游模型中的可行性与Hopf分岔

中文摘要 AI 辅助

我们比较了通过将相同的离散延迟分配给不同项而获得的基于污染的三变量旅游模型的八个变体。延迟可以进入三个位置：威慑项中的游客因子、污染感知或游客驱动的增长与再投资。当每个非负初始历史产生的解在未来所有时间内存在并保持非负时，我们称该放置为可行的。对于每个$\ au>0$，可行性恰好当威慑项中的游客因子是当前的时成立，这在八个放置中的四个中出现。在这四个可行放置中的三个中，正平衡对于每个延迟都是局部渐近稳定的。在第四个——感知滞后模型，具有延迟的污染感知但当前的游客——特征根的共轭对在有限临界延迟处穿过虚轴，对于每组正参数。平衡随后失去稳定性，并且随着延迟增加不会重新稳定。中心流形约简和数值参数扫描表明，超临界和亚临界Hopf分岔都可能发生。游客延迟放置，最接近早期的延迟旅游模型，可以在附加条件下经历局部Hopf分岔，但它不能对所有初始历史保持非负性。

英文摘要

We compare eight variants of a three-variable pollution-based tourism model obtained by assigning the same discrete delay to different terms. The delay may enter three slots: the visitor factor in the deterrence term, pollution perception, or visitation-driven growth and reinvestment. We call a placement feasible when every nonnegative initial history produces a solution that exists for all future time and remains nonnegative. For every $τ>0$, feasibility holds exactly when the visitor factor in the deterrence term is current, which occurs in four of the eight placements. In three of these four feasible placements, the positive equilibrium is locally asymptotically stable for every delay. In the fourth -- the perception-lag model, with delayed pollution perception but current visitation -- a conjugate pair of characteristic roots crosses the imaginary axis at a finite critical delay for every set of positive parameters. The equilibrium then loses stability and does not restabilise as the delay increases. A center-manifold reduction and numerical parameter sweep show that both supercritical and subcritical Hopf bifurcations can occur. The visitor-delayed placement, closest to earlier delayed-tourism models, can undergo a local Hopf bifurcation under additional conditions, but it does not preserve nonnegativity for all initial histories.

发表机构

• Marmara University（马尔马拉大学）
• Turkish Naval Academy, National Defence University（土耳其海军学院，国防大学）

机构由 AI 辅助整理，请以论文原文为准。

补充信息

备注

25 pages, 9 figures