Lotka-Volterra Systems with Periodic Orbits

Lotka-Volterra systems associated with skew-symmetric interaction between species are studied. We pick up some form of this model provided with conserved quantities, which makes all the solutions to be periodic-in-time except for the equilibrium. This class is explicitly given by a set of algebraic conditions on coefficients. If the system takes N components, we have 2N-3 and 2N-1 degrees of freedom without and with linear terms, respectively.