A Leslie population model for two generations is investigated by qualitative analysis and numerical simulation. For the different parameters a and b in the model, the dynamics of the system are studied, respectively. It shows many complex dynamic behavior, including several types of bifurcations leading to chaos, such as period-doubling bifurcations and Neimark–Sacker bifurcations. With the change of parameters, attractor crises and chaotic bands with periodic windows appear. The largest Lyapunov exponents are numerically computed and can verify the rationality of the theoretical analysis.

中文翻译：

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离散种群模型的分叉与混沌

通过定性分析和数值模拟研究了两代莱斯利种群模型。对于模型中不同的参数a和b，分别研究了系统的动力学特性。它显示了许多复杂的动态行为，包括导致混乱的几种分叉类型，例如周期倍增分叉和Neimark-Sacker分叉。随着参数的变化，出现吸引子危机和带有周期性窗口的混沌带。最大的李雅普诺夫指数被数值计算，可以验证理论分析的合理性。