(A)-parameter sweep of the Hindmarsh-Rose model based on the spike-counting approach. The color-coded bar to the right gives the spike-number range. The diagram clearly shows the boundaries of the spike-addition sequence, and the border between square-wave and plateau-like bursting. It also reveals the clove-shape structure of the zones of chaotic bursting which adjoin to the regions of tonic-spiking. (B) Same-range screening based on the evaluation of the the duty-cycle of bursting. The duty cycle value comes close to one near the boundary between bursting and tonic-spiking and drops close to zero near the border of the spiking region. Compare (A) and (B) with the screening diagram based on the Lyapunov exponents for solutions of the model in Figure 4 below.
Barrio and Shilnikov The Journal of Mathematical Neuroscience 2011 1:6 doi:10.1186/2190-8567-1-6