标题： 共振特性与三阶离散Logistic生态系统的混沌动力学：分岔点附近的邻域分析 显示英文标题

标题： Resonance properties and chaotic dynamics of a three-dimensional discrete logistic ecological system within the neighborhoods of bifurcation points

摘要： 本文中，我们深入研究了一类三维Logistic生态模型的动力学性质。 首先，利用多项式的完全判别理论，我们对每个不动点进行拓扑分类，并探讨相应系统在不动点附近的稳定性。然后借助分歧与正规型理论，讨论了不动点附近所有可能的余维-1分歧，即跨临界、倍周期和Neimark-Sacker分歧，并进一步证明系统可以经历余维-2分歧，特别是1:2、1:3、1:4强共振以及弱共振Arnold舌区。此外，严格分析了Marotto意义下的混沌行为。数值模拟被用来验证理论结果，并展示所识别出的复杂动力学现象。 显示英文摘要

摘要： In this paper, we delve into the dynamical properties of a class of three-dimensional logistic ecological models. By using the complete discriminant theory of polynomials, we first give a topological classification for each fixed point and investigate the stability of corresponding system near the fixed points. Then employing the bifurcation and normal form theory, we discuss all possible codimension-1 bifurcations near the fixed points, i.e., transcritical, flip, and Neimark-Sacker bifurcations, and further prove that the system can undergo codimension-2 bifurcations, specifically 1:2, 1:3, 1:4 strong resonances and weak resonance Arnold tongues. Additionally, chaotic behaviors in the sense of Marotto are rigorously analyzed. Numerical simulations are conducted to validate the theoretical findings and illustrate the complex dynamical phenomena identified.