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本文对一种海-气耦合非线性模型运用稳定性分析、拟能函数和Melinikov函数进行了理论分析,讨论了该系统的振荡、分岔和非周期性态。结果表明,当系统拟能最小时,具有有界的稳定周期解;系统拟能最大时,将出现分岔。考虑交叉因子作用时,系统有3个平衡态。考虑阻尼作用后,通过Melinikov函数导出的系统出现分岔的参数方程说明,系统存在唯一的不稳定极限环。
In this paper, the stability analysis, quasi-energy function and Melinikov function are applied to a nonlinear model of sea-atmosphere coupling, and the oscillation, bifurcation and aperiodic states of the system are discussed. The results show that the system has a bounded and stable periodic solution when the system quasi-energy is the smallest, and the bifurcation will occur when the system can be maximal. When considering the role of cross-factor, the system has three equilibrium states. After considering the damping effect, the parameter equation of bifurcation of the system derived by Melinikov function shows that the system has a unique unstable limit cycle.