摘要：We first study the distribution of the zeros of a fourth-degree
exponential polynomial. Then we apply the obtained results to a
simplified bidirectional associated memory (BAM) neural
network with four neurons and multiple time delays. By taking the
sum of the delays as the bifurcation parameter, it is shown that
under certain assumptions the steady state is absolutely stable.
Under another set of conditions, there are some critical values of
the delay, when the delay crosses these critical values, the Hopf
bifurcation occurs. Furthermore, some explicit formulae
determining the stability and the direction of periodic solutions
bifurcating from Hopf bifurcations are obtained by applying the
normal form theory and center manifold reduction. Numerical
simulations supporting the theoretical analysis are also included.
