The authors in [7] shown numerically the existence of a limit cycle surrounding the unstable node that system (1) has in the positive quadrant for specific values of the parameters. System (1) isone of the Belousov-Zabotinsky dynamical models. The objective of this paper is to prove that system (1), when in the positive quadrant Q has an unstable node or focus, has at least one limit cycle and, when f = 2/3, q = E²/2 and E > 0 suffciently small this limit cycle is unique.