This paper considers the existence of periodic solutions in space, in a particular case the system of differential equations describing the Chua circuit. Determine their equilibrium; linearize the system and thoroughly study the roots of the characteristic polynomial p( lambda) = lambda3 + ( alphac + 1) lambda2 + (alphac 􀀀 alpha + beta) lambda + alpha betac = 0, giving necessary conditions for each of the parameters alpha, beta and c. As in ordinary nonlinear determining global asymptotic stability in the equilibrium points differential systems is particularly important, build a Lyapunov function for the linear system under certain conditions, showing that the equilibrium point is asymptotically stable since the derivative of the Lyapunov function is less than zero.