Stability of a basic biological neural circuit

Considers a basic biologically plausible neural circuit that employs supragranular self-gain, negative feedback via inhibitory infragranular neuron. Such circuitry has been used as fundamental building blocks in modular neural networks. The authors first examine the conditions for stability of a nonadaptive model of such a circuit. The authors then examine the adaptive model employing a modified BCM learning rule. The authors show that the adaptive loop is stable under interestingly simple and reasonable conditions relating the self-gain to the neuron time constants, the synaptic adaptation rates, and the loop gain. The result lays solid foundation for the investigation of more complex recurrent modular neural networks.