Abstract: The classical Lotka-Volterra model study focuses only on simple interspecific competition or simple interspecific cooperation. Due to the complexity of the real environment and the diversity of the relationship between biological populations, the interrelationship between populations is often not a single one but a mixture of multiple relationships. In this paper, a class of two-species Lotka-Volterra competition-cooperation hybrid system is established. The competitive relationship and cooperative relationship occur among the two populations, which are alternately affected by environmental impact in different time intervals. By constructing appropriate Lyapunov functions and analysis, sufficient criterion is obtained for the global asymptotic stability of the system's positivity, bounded and positive equilibrium point, then data is given for simulation to verify the conclusion. Through the study, it is found that the competition-cooperation model has more dynamic behavior than the single competition model or cooperative model, and the biological population shows more survivability, which is more consistent with the real environment.

Key words: competition-cooperation hybrid system, population, positive, boundedness, global asymptotic stability