Geometric method for a global repellor in competitive Lotka–Volterra systems

The geometric method of involving the relative positions of the nullcline planes is used to analyze the global asymptotic behavior of solutions of autonomous Lotka–Volterra competitive systems. Some observations about limit sets are made and, based on these observations, new criteria are established for the system to have a single point global repellor. Clearly, these criteria can be used to preclude the existence of nonconstant periodic solutions.