  The network studied here is based on a standard model in physics, but it
appears in various applications ranging from spintronics to neuroscience. When
the network is forced by an external signal common to all its elements, there
are shown to be two potential (gradient) functions: One for amplitudes and one
for phases. But the phase potential disappears when the forcing is removed. The
phase potential describes the distribution of in-phase/anti-phase oscillations
in the network, as well as resonances in the form of phase locking. A valley in
a potential surface corresponds to memory that may be accessed by associative
recall. The two potentials derived here exhibit two different forms of memory:
structural memory (time domain memory) that is sustained in the free problem,
and evoked memory (frequency domain memory) that is sustained by the phase
potential, only appearing when the system is illuminated by common external
forcing. The common forcing organizes the network into those elements that are
locked to forcing frequencies and other elements that may form secluded
sub-networks. The secluded networks may perform independent operations such as
pattern recognition and logic computations. Various control methods for shaping
the network's outputs are demonstrated.
