ABSTRACT
The two-dimensional Lotka-Volterra systems are well understood: If the two species cooperate or compete there are no periodic orbits, and all bounded trajectories of the flow converge to a fixed point. This chapter analyses some of the geometric results that have recently been developed to study competitive Lotka-Volterra systems. One way to geometrically capture the algebraic simplicity of the autonomous Lotka-Volterra equations is by the nullclines of the system. The chapter describes tools that are designed to capture the algebraic simplicity of the autonomous equations in new ways, in order to deduce some of the dynamical information that nullcline analysis cannot provide as the dimension of the system increases.
