Logistic系统跃迁率的时间延迟效应

本文研究了时间延迟对Logistic系统从亚稳态跃迁到稳定态的跃迁率的影响. 假设在细胞演化过程中细胞衰减存在时间延迟,利用小延迟时间条件下一阶近似方法和最陡下降法导出了系统的跃迁率解析式. 数值计算结果表明,内噪声,外噪声和内外噪声之间的关联促使系统从亚稳态跃迁到稳定态, 而时间延迟阻碍了系统从亚稳态到稳定态的跃迁, 即时间延迟增强了系统亚稳态的稳定性. 关键词： Logistic模型 跃迁率 时间延迟 噪声

Effects of time delay on transition rate of state in an increasing process of Logistic system

The effects of time delay on transition rate from metastable state to stable state in a Logistic system are investigated. On the assumption that there is a delay time in the decay process of cell evolution, the expression of the transition rate is derived in the first order approximation under the condition of the small delay time and the steepest-descent approximation. The numerically calculated results indicate that the additive noise, the multiplicative noise and the correlations between additive and multiplicative noises enhance the system transition from metastable state to stable state. However, such a transition is restrained by the time delay, i.e., the time delay enhances the stability of the system.