Chaotic solutions in the quadratic integrate-and-fire neuron with adaptation

The quadratic integrate-and-fire (QIF) model with adaptation is commonly used as an elementary neuronal model that reproduces the main characteristics of real neurons. In this paper, we introduce a QIF neuron with a nonlinear adaptive current. This model reproduces the neuron-computational features of real neurons and is analytically tractable. It is shown that under a constant current input chaotic firing is possible. In contrast to previous study the neuron is not sinusoidally forced. We show that the spike-triggered adaptation is a key parameter to understand how chaos is generated.

[1]  K Aihara,et al.  Periodic and non-periodic responses of a periodically forced Hodgkin-Huxley oscillator. , 1984, Journal of theoretical biology.

[2]  Eugene M. Izhikevich,et al.  Simple model of spiking neurons , 2003, IEEE Trans. Neural Networks.

[3]  K. Pakdaman,et al.  Chaotic firing in the sinusoidally forced leaky integrate-and-fire model with threshold fatigue , 2004 .

[4]  P H E Tiesinga,et al.  Precision and reliability of periodically and quasiperiodically driven integrate-and-fire neurons. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Eugene M. Izhikevich,et al.  Which model to use for cortical spiking neurons? , 2004, IEEE Transactions on Neural Networks.

[6]  S. Thorpe,et al.  Spike times make sense , 2005, Trends in Neurosciences.

[7]  Boris S. Gutkin,et al.  Dynamics of Membrane Excitability Determine Interspike Interval Variability: A Link Between Spike Generation Mechanisms and Cortical Spike Train Statistics , 1998, Neural Computation.

[8]  Hatsuo Hayashi,et al.  Chaotic behavior in the Onchidium giant neuron under sinusoidal stimulation , 1982 .

[9]  J. Yorke,et al.  Period Three Implies Chaos , 1975 .

[10]  Eugene M. Izhikevich,et al.  Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting , 2006 .

[11]  Jonathan Touboul,et al.  Bifurcation Analysis of a General Class of Nonlinear Integrate-and-Fire Neurons , 2008, SIAM J. Appl. Math..

[12]  Boris S. Gutkin,et al.  The Effects of Spike Frequency Adaptation and Negative Feedback on the Synchronization of Neural Oscillators , 2001, Neural Computation.

[13]  Eugene M. Izhikevich,et al.  Neural excitability, Spiking and bursting , 2000, Int. J. Bifurc. Chaos.

[14]  S. Coombes.  Liapunov exponents and mode-locked solutions for integrate-and-fire dynamical systems , 1999 .

[15]  G D Lewen,et al.  Reproducibility and Variability in Neural Spike Trains , 1997, Science.

[16]  N. Brunel,et al.  From subthreshold to firing-rate resonance. , 2003, Journal of neurophysiology.

[17]  F. R. Marotto.  Snap-back repellers imply chaos in Rn , 1978 .

[18]  Wulfram Gerstner,et al.  Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. , 2005, Journal of neurophysiology.

[19]  André Longtin,et al.  Interspike Interval Correlations, Memory, Adaptation, and Refractoriness in a Leaky Integrate-and-Fire Model with Threshold Fatigue , 2003, Neural Computation.

[20]  F. R. Marotto.  On redefining a snap-back repeller , 2005 .

[21]  O. Prospero-Garcia,et al.  Reliability of Spike Timing in Neocortical Neurons , 1995 .

[22]  Romain Brette,et al.  The Cauchy problem for one-dimensional spiking neuron models , 2008, Cognitive Neurodynamics.

[23]  Emmanuel Guigon,et al.  Reliability of Spike Timing Is a General Property of Spiking Model Neurons , 2003, Neural Computation.

[24]  Bard Ermentrout,et al.  Type I Membranes, Phase Resetting Curves, and Synchrony , 1996, Neural Computation.

[25]  G. Ermentrout,et al.  Parabolic bursting in an excitable system coupled with a slow oscillation , 1986 .

[26]  Michael J. Berry,et al.  The structure and precision of retinal spike trains. , 1997, Proceedings of the National Academy of Sciences of the United States of America.