  A new model of neural networks described by the memristive and diffusive
Hindmarsh-Rose equations is proposed. Globally dissipative dynamics is shown
with absorbing sets in the state spaces. Through sharp and uniform grouping
estimates and by leverage of integral inequalities tackling the linear network
coupling against the memristive nonlineariry, it is rigorously proved that
exponential synchronization at a uniform convergence rate occurs when the
coupling strengths satisfy the threshold conditions quantitatively expressed by
the parameters.
