Bivalent BAM theorem -This impliesxUs so the product is positive: AS,(x)[x+1-U,>0 So+-Lk<0 for every state change. -Since L is bounded,L behaves as a Lyapunov function for the additive BAM dynamical system defined by before. Since the matrix M was arbitrary,every matrix is bidirectionally stable.The bivalent BAM theorem is proved. 1010 Bivalent BAM theorem This implies so the product is positive: i k xi U +1 0 1  −  + ( )[ ] i k Si xi xi U So for every state change. 0 Lk+1 − Lk  Since L is bounded,L behaves as a Lyapunov function for the additive BAM dynamical system defined by before. Since the matrix M was arbitrary,every matrix is bidirectionally stable. The bivalent BAM theorem is proved