Further Studies on the Dynamics of a Lotka–Volterra Competitor–Competitor–Mutualist System with Time-Varying Delays

Abstract

In this paper, a Lotka–Volterra (L-V) competitor–competitor–mutualist system with time-varying delays is studied. Some dynamical behaviors of the considered system are investigated. Firstly, we obtain the boundedness, permanence and periodic solution of the system using the comparison principle of differential equations and inequality estimation method. Then, the global attractiveness of the system is analyzed by multiple Lyapunov functionals. Meanwhile, the existence and global attractivity of positive periodic solutions is derived. In the third section, in order to validate the practicability and feasibility of the obtained theoretical results, we conducted numerical simulations using MATLAB function ddesd. Finally, the fourth section is where conclusions are drawn.

Keywords

• permanence
• global attractivity
• time-varying delay
• Lyapunov functional
• periodic solution
• Lotka–Volterra competitor–competitor–mutualist system