Using continuation methods and bifurcation theory, we study the exact multiplicity of periodic solutions, and the global solution structure, for periodic problems of first order. The results are applied to a population model with fishing, and to the existence and stability of limit cycles. We also describe in detail our numerical computations of curves of periodic solutions, and of limit cycles.

中文翻译：

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一阶周期问题的整体解曲线及其应用

利用延续方法和分叉理论，我们研究了一阶周期问题的周期解的精确多重性以及整体解的结构。将结果应用于带捕鱼的种群模型，以及极限环的存在和稳定性。我们还将详细描述周期解曲线和极限环的数值计算。