The phenomenological neuron model proposed by Hindmarsh and Rose may be seen either as a generalization of the Fitzhugh equations or as a simplification of the physiologically realistic model proposed by Hodgkin and Huxley. It is capable of mimicking almost all the behaviors exhibited by real biological neurons, such as spiking, bursting, and irregular behaviors.
This Demonstration allows you to vary the four parameters independently to explore the different dynamical behaviors of the model.
The roles played by the system parameters are the following: mimics the membrane input current for biological neurons; allows one to switch between bursting and spiking behaviors and to control the spiking frequency; controls the speed of variation of the slow variable; governs adaptation: a unitary value of determines spiking behavior without accommodation and subthreshold adaptation, whereas values around 4 give strong accommodation and subthreshold overshoot.
Two-dimensional bifurcation diagrams can be found in the following paper:
M. Storace, D. Linaro, and E. de Lange, "The Hindmarsh-Rose Neuron Model: Bifurcation Analysis and Piecewise-Linear Approximations," Chaos, 18, 2008 pp. 1–10 033128.
More information on the model and on its bifurcations can be found on our research page.