Properties of meromorphic solution of the Lotka-Volterra equations

In this paper, utilizing value distribution theory of Nevanlinna, we obtain results by showing different properties of complex-valued solutions of Lotka-Volterra equations dx/dt = ax - bxy dy/dt = cxy - dy where x is the prey population, y is the predator population, and a, b, c, and d are positive constants. Moreover, we obtain a result finding the sufficient conditions for periodic complex-valued solutions of Lotka-Volterra equations. Furthermore, we show that periodic complex-valued solution is stable if and only if the real part of the complex eigenvalues of the matrix [GRAPHICS] are negative.