To overcome the complexity of the Hodgkin-Huxley model , Richard FitzHugh introduced a second-order differential equations which appears to be too simplified . Then James Hindmarsh and Malcom Rose added a third equation to limit the neuron firing and got the model 
where x is the membrane potential, y the recovery variable (quantifying the transport of sodium and potassium through fast ion channels) and z an adaptation current which gradually hyperpolarizes the cell (it corresponds to the transport of other ions through slow channels). For appropriate parameter values, the Hindmarsh-Rose system produces a chaotic attractor (Fig. 1a) characterized by a first-return map to the Poincaré section
which is smooth and unimodal (Fig. 1b). This behavior is obtained after a period-doubling cascade when the applied current I is decreased. The parameter values used for producing this chaotic attractor are a=1, b=3, c=1, d=5, r=0.001, s=4, and I=3.318.
 A. L. Hodgkin & A. F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, Journal of Physiology, 177, 500-544, 1952.
 R. FitzHugh, Impulses and physiological states in theoretical models of nerve membrane, Biophysical Journal, 1, 445-466, 1961.
 J. L. Hindmarsh & R. M. Rose, A model of neuronal bursting using three coupled first order differential equations, Proceedings of the Royal Society of London B, 221, 87-102, 1984.