Nonlinear Dynamics

, Volume 97, Issue 4, pp 2091–2105 | Cite as

Bifurcations of enhanced neuronal bursting activities induced by the negative current mediated by inhibitory autapse

  • Yuye Li
  • Huaguang GuEmail author
  • Xueli Ding
Original paper


In contrast to the traditional viewpoint that inhibitory effect can often induce the reduction of neural firing activities, negative self-feedback current mediated by inhibitory autapse is identified to enhance neuronal bursting activities in the Chay model composed of fast and slow subsystems. With increasing autaptic strength of the autapse, bursting patterns exhibit period-adding bifurcations, which leads to the increase in the mean firing frequency. Such a phenomenon can be well interpreted with fast–slow variable dissection and bifurcation analysis to the bursting patterns. The initial and termination phases of the burst correspond to a saddle-node bifurcation and a saddle-homoclinic (SH) bifurcation of the fast subsystem, respectively. With increasing the autaptic strength, the termination phase of the burst delays and the initial phase remains nearly unchanged. Therefore, the width of the burst becomes wider to contain more spikes, which leads to the period-adding bifurcations and the increases of mean firing frequency. The detailed relationship between the delay of termination phase (SH point) and the characteristic of the inhibitory autaptic current is identified. Moreover, the distinction between the present paper and the previous investigations of the enhancement of bursting activities induced by inhibitory current with time delay is discussed. Based on the results that inhibitory autapse without time delay can enhance bursting activities via bifurcation mechanism, a novel case of nonlinear dynamics in contrast to the traditional viewpoint of the inhibitory effect, a possible function of the autapse, a novel potential measure to modulate bursting activities are present.


Bifurcation Neural firing Inhibitory effect Autapse Fast–slow variable dissection 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsChifeng UniversityChifengChina
  2. 2.Institute of Applied MathematicsChifeng UniversityChifengChina
  3. 3.School of Aerospace Engineering and Applied MechanicsTongji UniversityShanghaiChina
  4. 4.Department of Basic EducationFuyang Institute of TechnologyFuyangChina

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