Abstract: Normal form equations in bifurcation theory are used to design and syn-thesize analog neural networks which can store st at ic or oscillating memory patterns.For the network storing static memory patterns,the normal form equations are of the pitch- fork bifurcation type. If the stored patterns are periodically oscillating, the normal form equations are of the mutiple Hopf bifurcation type. The synaptic weights obtained from the coefficients of the normal form equations which satisfy the designing restraint...