Hindmarsh-Rose model

X.-J.Wang Genesis of bursting oscillations in the Hindmarsh-Rose model and ho-moclinicity to a chaotic saddle. Physica D 1993, 62 263-274. 

C.2. 14. Study the equilibria of the Hindmarsh-Rose model of neuronal activity [177]... 

A theoretical analysis of Eq. (13.6) provides the domains of control, i.e. the ranges of delay time and amplification in the feedback loop for which the control is effective. These results are in a good correspondence with the numerical simulation of the ensemble dynamics with different neuron models used for the description of individual units (Bonhoefer - van der Pol or Hindmarsh-Rose equations [21], Rulkov map model [42]). 

Oscillations of the bursting type have been modelled mainly in neurobiology, whieh is the field where they are most frequently observed. These models consist in modifications of the Hodgkin Huxley equations, which generally take into account the effect of Ca "" and the slow, cyclical variation of some ionic conductances (Plant Kim, 1976 Plant, 1978 Carpenter, 1979 Hindmarsh Rose, 1984 Chay Rinzel, 1985 Ermentrout Koppell, 1986 Rinzel Lee, 1986 Canavier etal, 1991 Smolen Keizer, 1992 Destexhe, Babloyantz Sejnowski, 1993 Bertram, 1994). 

J. L. Hindmarsh and R. M. Rose. A model for neuronal bursting using three coupled first order differential equations. Proc. Roy. Soc. London Ser. B,... 

Hindmarsh, J.L. R.M. Rose. 1982. A model of the nerve impulse using two first order differential equations. Nature 296 162-4. 

Rose, R.M. J.L. Hindmarsh. 1989a. The assembly of ionic currents in a thalamic neuron. I. The three-dimensional model. Proc. R. Soc. Lond. B 237 267-88. 

A second model [Hindmarsh and Rose, 1982b] sought to include the phenomenon of bursting by adding a third variable. The model had the following form ... 

Hindmarsh, J. L. and Rose, R. M. [1984] A model of neuronal bursting using three cioupled first order differential equations , Proc. R. Soc. Lond. B221, 87-102. 

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