Global-in-time behavior of Lotka-Volterra system with diffusion Takashi SuzukiYoshio Yamada MSC2010. 35K5735B40Lotka-Volterra system!-limit setblowup analysisperiodic-in-time solutionthermodynamics We study the global-in-time behavior of the Lotka-Volterra system with diffusion. In the first category, the interaction matrix is skew-symmetric and the linear terms are non-increasing. There, the solution exists globally in time with compact orbit, provided that $n\leq2$, where $n$ denotes the space dimension. Under the presence of entropy, its $\omega$-limit set is composed of a spatially homogeneous orbit. Furthermore, any spatially homogeneous solution is periodic in time, provided with constant entropy. In the second category, the interaction matrix exhibits a dissipative profile. There, the solution exists globally in time with compact orbit if $n\leq3$. Its $\omega$-limit set, furthermore, is contained in spatially homogeneous stationary states. In particular, no periodic-in-time solution is admitted. Indiana University Mathematics Journal 2015 text pdf 10.1512/iumj.2015.64.5460 10.1512/iumj.2015.64.5460 en Indiana Univ. Math. J. 64 (2015) 181 - 216 state-of-the-art mathematics http://iumj.org/access/