Eugene M. Izhikevich presented a model that reproduces spiking and bursting behavior of known types of cortical neurons . The model combines the biologically plausibility of the dynamics underlying the Hodgkin–Huxley model  and the computational efficiency of integrate-and-fire neurons. As initiated by Bard Ermentrout and Nancy Kopell , this model is made of an oscillator producing slow oscillations combined with a switching mechanism for reproducing the bursting phenomenon . The model equations - as proposed in Ref.  - are
where the switching mechanism is introduced as follows
Variable x represents the membrane recovery which accounts for the activation of K+ ionic currents and inactivation of Na+ ionic currents, and it provides negative feedback to the membrane potential of the neuron y. Synaptic currents or injected dc-currents are delivered via the variable Isyn. The part 0.04y2+5y+140 was obtained by fitting the spike initiation dynamics of a cortical neuron so that the membrane potential is expressed in mV and the time in ms.
Using parameter values a=0.2, b=2, c=-56, d=-16 and Isyn=-99, and initial conditions as
a chaotic attractor can be obtained (Fig. 1). It is characterized by a first-return map to a Poincaré section made of four branches, more or less as can be found in the Rössler system .
 E. M. Izhikevich, Simple model of spiking neurons, IEEE Transactions on Neural Networks, 14 (6), 1569-1572, 2003.
 A. L. Hodgkin & A. F. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve, The Journal of Physiology, 117 (4), 500-544, 1952.
 G. B. Ermentrout & N. Kopell, Parabolic bursting in an excitable system coupled with a slow oscillation, SIAM Journal of Applied Mathematics, 46 (2), 233-253, 1984.
 E. M. Izhikevich, Neural, excitablity, spiking and bursting, International Journal of Bifurcation & Chaos, 10, 1171-1266, 2000.
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