A study of dynamic behavior of a recurrent neural network for control

The dynamic behavior of a two-neuron recurrent network formulated from biological observations is studied. Different parameters that will affect the dynamic behavior of the network include decaying constant, synaptic weight, initial state of neuron, input to the system, and the activation function. The issues of stability, equilibrium state, and convergence time are explored. The convergence time is affected by the choice of decaying constant. In addition, the discontinuous activation function presents several favorable features over the continuous sigmoid function from the control point of view. Because of the discontinuity, equilibrium state can be separated into active region and inactive region. The active region can be triggered through the excitatory input, if the initial state is in the inactive region. The state of the equilibrium point is `directly modulated by the input, which implies a unique input-output relationship