Bursting, spiking, and chaotic regimes in a 3D conductance model
3.20
0.0060
4.0
-1.60
Membrane Voltage x
—
Recovery var y
—
Slow adapt z
—
Spike rate (Hz)
—
Hindmarsh-Rose model: a three-variable system (x=membrane voltage, y=fast recovery, z=slow adaptation) capturing the rich dynamics of real neurons. The equations ẋ = y − ax³ + bx² − z + I, ẏ = c − dx² − y, ż = r[s(x−x_R) − z] produce quiescence, tonic spiking, square-wave bursting, and deterministic chaos depending on parameters. Bursting arises from slow oscillation of z modulating fast x-y spike cycles. This type of behavior is seen in thalamic relay neurons, hippocampal interneurons, and invertebrate central pattern generators. The phase portrait (bottom, x vs z) reveals the slow manifold and burst trajectory.