Grazing bifurcation and mode-locking in reconstructing chaotic dynamics with a leaky integrate-and-fire model
We examined the firing patterns of a chaotically forced leaky integrate-and-fire (LIF) model, and the validity of reconstructing input chaotic dynamics from an observed spike sequence. We generated inputs to the model from the Rössler system at various values of the bifurcation parameter, and carried out numerical simulations of the LIF model forced by each input. For both chaotic and periodic inputs, therotation numbers and the Lyapunov exponents were calculated to investigate the mode-locked behavior of the system. Similar behaviors as in the periodically forced LIF model were also observed in the chaotically forced LIF model. We observed (i)grazing bifurcation with the emergence of qualitatively distinct behaviors separated by a certain border in the parameter space, and (ii) modelocked regions where the output spike sequences are modelocked to the chaotic inputs. We found that thegrazing bifurcation is related to the reconstruction of chaotic dynamics with the LIF. Our results can explain why the shape of the partially reconstructed ISI attractor, which was observed in previous studies.
Key wordsLeaky integrate-and-fire model Chaos Interspike interval Attractor reconstruction Grazing bifurcation Mode-locking
Unable to display preview. Download preview PDF.
- 1.Takens F (1981) Detecting strange attractors in turbulence. In: Dynamical systems and turbulence. Springer, Berlin, pp 366–381Google Scholar
- 3.Saner T (1997) Reconstruction of integrate-and-fire dynamics. In: Nonlinear dynamics and time series. American Mathematical Society, Providence, p 63–75Google Scholar
- 14.Budd CJ (1996) Non-smooth dynamical systems and the grazing bifurcation. In: Nonlinear mathematics and its applications. Cambridge University Press, Cambridge, pp 219–235Google Scholar
- 15.Hodgkin AL (1948) The local electric changes associated with repetitive action in a non-modulated axon. J Physiol 107:165–181Google Scholar
- 16.Rinzel J, Ermentrout GB (1989) Analysis of neural excitability and oscillations. In: Koch C, Segev I (eds) Methods in neuronal modeling. MIT Press, Cambridge.Google Scholar