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一类生物入侵模型的解析极限环解
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Abstract:
本文利用平方广义谐波函数摄动法研究了一类具有对流–反应–扩散类型的单种群生物入侵模型，求得了该系统极限环解的近似表达式，并得到了极限环幅值与控制参数之间的关系。利用此关系预测了系统在不同参数下的极限环振幅，通过将本方法计算所得结果与数值结果进行比较，验证了所得结果的有效性和可靠性。该结果表明平方广义谐波函数摄动法亦可推广至一类无限维动力系统Hopf分岔的解析定量分析，为无限维动力系统的研究相提供了新的思路和参考方法。
In this paper, a single species biological invasion model with convection diffusion reaction type is studied by using the square generalized harmonic function perturbation method. The approximate expression of the limit cycle solution of the system is obtained, and the relationship between the limit cycle amplitudes and the control parameters is also obtained. Based on this relationship, the limit cycle amplitudes of the system under different parameters are predicted. By comparing the results calculated by this method with the numerical results, the effectiveness and reliability of the results are verified. The medium and long-term prediction of the population density development of a class of species and the effective control of Hopf bifurcation behavior are realized, which provides a new idea and reference method for the analytical and quantitative study of Hopf bifurcation of a class of infinite dimensional dynamic systems.
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