Analytic solutions to a family of Lotka-Volterra related differential equations (Q1580223)

The paper deals with a complete reduction of the Lotka-Volterra problem to an integral quadrature and its exploration of this quadrature. A family of first-order autonomous ordinary differential equations related to the Lotka-Volterra system is derived, and the analytic solutions to these systems are given. Moreover the constant of the motion for this family is given, and a simple transformation is found to take this invariant into Hamiltonian form.