中文摘要：

针对非定常通气超空泡的不稳定性，采用分叉与突变理论分析通气超空泡失稳现象发生的机理。基于Logvinovich空泡截面膨胀独立性原理及通气质量平衡方程，得出联系非定常通气超空泡长度及空化数的积分方程。根据积分思想，将积分方程分解为两个第一类Volterra积分求解，得出线性小扰动系统，对静态分叉引发的状态突变进行定性分析，并通过数值仿真进行了验证。理论分析及数值仿真结果表明，非定常通气超空泡在平衡点处呈现的跨临界分叉将导致非定常通气超空泡在分叉点处产生突变。此现象揭示了稳定通气超空泡在临界值处改变通气参数所导致的空泡失稳的机理，有助于超空泡航行体稳定航行控制系统的设计。

英文摘要：

Aiming at the instability of the unsteady ventilated supercavity, the bifurcation and catastrophe theory methodology is adopted to analyze the instability mechanism of the ventilated supercavity. Based on Logvinovich independence principle of the cavity section expansion and the ventilated mass balance equation, the integral equation that contacts the length of the unsteady ventilated supercavity and cavity number is obtained. According to calculus thought, the integral equation is divided into two first class Volterra equations to get the solution and the linear small disturbance system. Then the status catastrophe caused by static bifurcation is discussed and verified through numerical simulations. Theoretical analysis and numerical simulation results show that transcritical bifurcation at the equilibrium points of the unsteady ventilated supercavity leads to the generation of catastrophe at the bifurcation point. These phenomena reveal the instability mechanism of the stable ventilated supercavity as changing ventilatation parameters at the system for SUlaercavitatin vehicle. critical value, which are benefit to design stable control