An N-barrier maximum principle for autonomous systems of $n$ species and   its application to problems arising from population dynamics
  We show that the N-barrier maximum principle (NBMP) remains true for $n$ $(n>2)$ species. In addition, a stronger lower bound in NBMP is given by employing an improved tangent line method. As an application of NBMP, we establish a nonexistence result for traveling wave solutions to the four species Lotka-Volterra system. 
Chiun-Chuan Chen, Li-Chang Hung and Chen-Chih Lai
math.AP