具时滞和反馈控制的Lotka-Volterra合作系统的全局稳定性

Global stability of a Lotka-Volterra cooperation system with time delays and feedback controls

研究一类具时滞和反馈控制的Lotka-Volterra合作系统。在不同时滞条件下,通过构建合适的Lyapunov函数,建立保证系统正平衡点全局稳定的充分条件。结果表明:时滞的存在并没有改变系统正平衡点全局稳定性的充分条件,因此,离散时滞属于无害时滞。

Consider a Lotka-Volterra cooperation system with time delays and feedback controls. By constructing suitable Lyapunov functions, sufficient conditions are established to ensure the global stability of the positive equilibrium of system with different time delays. The result shows that the existence of time delays does not change the sufficient conditions which ensure the global stability of the system. There-fore, the discrete time delays belong to harmless delays.