The complex dynamics of abnormal phenomenon of neural electronic oscillations induced by negative feedback

In traditional viewpoint, it is easy to achieve stable equilibrium for a system with negative feedback and stable oscillations for a system with positive feedback. In the present investigation of the nonlinear neural system, a novel viewpoint that negative feedback can induce stable equilibrium, i.e. the resting state, changed to oscillations, i.e. firing, is proposed. In a theoretical neuron model, inhibitory stimulation mediated by the negative impulsive current with enough strength can induce an action potential from the resting state near a Hopf bifurcation point and the after-potential with damping oscillations following the action potential. The strength threshold of the second negative impulsive current applied within the after-potential to evoke the second action potential exhibits damping oscillations as well with respect to the application phase of the current. After introducing negative feedback with time delay (τ) into the theoretical model to simulate the inhibitory autapse, the negative feedback current induced by an action potential is applied at the phase τ of the after-potential following the action potential. The negative feedback gain threshold to induce firing from the resting state exhibits characteristics of damping oscillations with increasing time delay corresponding to application phase of the current, which resembles the time delay induced-multiple coherence resonances. The oscillation period is associated with the period of strength threshold curve of the second impulsive current to evoke the second action potential from after-potential and the period of the firing near the Hopf bifurcation. Furthermore, the negative feedback can also induce complex dynamics such as the coexistence of the firing and resting state. The results of the present paper not only present a novel modulation effect of the negative feedback, which is a contrast to the tradition viewpoint, but also are helpful for understanding the potential functions of slow inhibitory autapse that can induce negative impulsive current with time delay in the real neural system. © 2019, Chinese Journal of Theoretical and Applied Mechanics Press. All right reserved.