We will study global properties of evolutional Lotka-Volterra system. We assume that the predatory efficiency is a function ofa character of species whose evolution obeys a quantitative genetic model. We will show that the structure ofa solution is rather different from that of a non-evolutional system.We will analytically show new ecological features of the dynamics.
P. A. Abrams and H. Matsuda, “Fitness Minimization and Dynamic Instability as a Consequence of Predator-Prey Coevolution,” Evolutionary Ecology, Vol. 11, No. 1, 1997, pp. 1-20. http://dx.doi.org/10.1023/A:1018445517101