随机激励下非线性时滞船舶横摇模型的随机分岔
Random Bifurcation of Nonlinear Time-Delay Ship Rolling Motion under Random Excitation
摘要: 本文研究了同时带有随机激励与时滞反馈控制的船舶横摇动力学模型。首先，分析了系统发生Hopf分岔的临界条件；其次，借助中心流形理论和最大Lyapunov指数，考察了系统的局部稳定性及随机D分岔的产生条件，并基于奇异边界理论对系统的全局稳定性进行了讨论；最后，通过数值模拟揭示了噪声强度与时滞系数对系统动力学行为的影响机制，从而验证了相关理论结果的正确性。
Abstract: This paper investigates a ship rolling dynamics model with both random excitation and time-delay feedback control. First, the critical conditions for the occurrence of Hopf bifurcations are analyzed. Second, using central manifold theory and the maximum Lyapunov exponent, the local stability of the system and the conditions for the occurrence of random D-bifurcation are investigated. The global stability of the system is discussed based on singular boundary theory. Finally, numerical simulations reveal the mechanisms by which noise intensity and time-delay coefficients influence the system’s dynamic behavior, validating the theoretical results.
文章引用：武昊宇. 随机激励下非线性时滞船舶横摇模型的随机分岔[J]. 应用数学进展, 2025, 14(10): 379-391. https://doi.org/10.12677/aam.2025.1410449

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