Many asteroids move in the belt between the orbits of Mars and Jupiter under the gravitational attraction of the Sun and planets in the Solar system. If one of these asteroids does not leave the belt during a period, it is considered to be temporarily stable on that time-scale. This paper aims to study the time-scales on which asteroids could stay in the main belt. A simplified situation is studied in which the initial orbital inclinations and the longitudes of the ascending nodes of the asteroids are set to zero. Numerical integration is used to study the temporal stability of the main-belt asteroids. In the integration, the distribution of the instability time for randomly generated particles can be fitted with a function. Thus a reasonable method is presented to choose an integration time-scale based on the percentage of the already unstable particles in relation to all unstable particles. A total of 151 000 particles are generated and then integrated for 8.09 × 106 yr. The integration data are used to train the probabilistic neural networks to predict the stability of particles. A temporal stability map in the a-e plane is obtained from the prediction results of the neural networks.

中文翻译：

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基于神经网络的主带小行星稳定性时间尺度预测

许多小行星在太阳和太阳系行星的引力作用下，在火星和木星轨道之间的带中移动。如果其中一颗小行星在一段时间内没有离开该带，则认为它在该时间尺度上暂时稳定。本文旨在研究小行星可能停留在主带的时间尺度。研究了一个简化的情况，其中小行星的初始轨道倾角和升交点的经度设置为零。数值积分用于研究主带小行星的时间稳定性。在积分中，随机生成的粒子的不稳定时间分布可以用一个函数拟合。因此，提出了一种合理的方法来选择基于已经不稳定粒子相对于所有不稳定粒子的百分比的积分时间尺度。总共产生了 151 000 个粒子，然后在 8.09 × 106 年的时间内进行了整合。积分数据用于训练概率神经网络以预测粒子的稳定性。从神经网络的预测结果获得ae平面中的时间稳定性图。