Paradoxical enhancement of neuronal bursting response to negative feedback of autapse and the nonlinear mechanism

Paradoxical phenomena such as synchronization and post inhibitory rebound spike induced by the inhibitory effects are important for both nonlinear science and neuroscience. In the present paper, a novel paradoxical example for the bursting activity modulated by the negative self-feedback of the inhibitory autapse and the dynamical mechanism are acquired in a theoretical model. As the inhibitory autaptic conductance increases, the burst duration becomes wide or the spike number per burst becomes large, which is different from the common viewpoint that the burst duration should become narrow or the spike number should become small. Meanwhile, the bursting patterns exhibit the transition from “fold/homoclinic” type, to “fold cycle/homoclinic” type, and to “point-point” type, which shows that the paradoxical phenomenon is not a special case for a specific bursting but a universal phenomenon for multiple bursting patterns. Furthermore, the paradoxical enhancement of bursting activity is well explained with the nonlinear dynamics such as the bifurcations of the fast subsystem, the amplitude of the stable limit cycle, and the eigenvalues of the stable focus. The results enrich the contents of nonlinear science and present a potential strategy to enhance the bursting activity of neuron with inhibitory autapse.