季节性繁殖物种在年周期环境中的传播动力学
Propagation Dynamics of a Single Species with Seasonal Breeding in Yearly Periodic Environment
DOI: 10.12677/aam.2025.145290, PDF,    科研立项经费支持
作者: 孙岩妹, 张玉香*：天津职业技术师范大学理学院，天津
关键词: 季节性繁殖；常–偏微分方程混合模型；传播速度；行波解；Seasonal Breeding； Hybrid ODE-PDE Model； Spreading Speed； Traveling Wave Solutions
摘要: 针对季节性繁殖种群的周期动力学问题，本文提出了一个依赖于时间的常–偏微分方程(ODE-PDE)混合模型。采用周期演化系统的动力学理论，对系统在无界空间中的传播速度和行波解的存在性问题进行研究，取得了具有单调出生函数的季节性繁殖种群入侵传播速度和行波解的存在性结果，得到了系统传播速度与行波的最小波速一致性结论，给出了传播速度的计算公式。数值模拟结果不仅验证了理论预测的准确性，还进一步探讨了繁殖季节长度对物种演化的影响。
Abstract: We propose a time-dependent hybrid ODE-PDE model to study the periodic population dynamics of a single species with short breeding season. By employing the dynamical theory of periodic evolution systems, we investigate the existence of the spreading speed and traveling wave solution of the model in an unbounded spatial domain. For monotonic birth functions, we establish the existence of invasion spreading speed and traveling waves in seasonal breeding population, prove the coincidence of the spreading speed and minimal wave speed of the traveling wave, and derive an explicit formula for calculating the spreading speed. The numerical simulation results not only validate the correctness of the theoretical predictions, but also provide further insights into the impact of the length of the breeding season on the population evolution.
文章引用：孙岩妹, 张玉香. 季节性繁殖物种在年周期环境中的传播动力学[J]. 应用数学进展, 2025, 14(5): 645-659. https://doi.org/10.12677/aam.2025.145290

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