Bursting in cerebellar stellate cells induced by pharmacological agents: Non-sequential spike adding
Fig 10
Bifurcation diagram of the fast subsystem, represented by the membrane voltage V, when hA is varied as a parameter and Ca is kept fixed at a random but physiologically-relevant value of 0.2 μM.
The Z-shaped curve (black) is the branch of equilibria of the fast subsystem consisting of three branches separated by two saddle-node bifurcations, denoted SN1 and SN2. The solid and dotted black lines indicate stable and unstable branches of equilibria, respectively. The lower and middle branches are of stable and saddle type, respectively. The upper branch is stable for lower values of hA and becomes unstable (of saddle type) at a subcritical Hopf bifurcation, denoted HB, where an envelope of unstable periodic orbits emanates and terminates at a homoclinic bifurcation (HC1). An isolated envelope of periodic orbits comprised of an upper and a lower ⊂-shaped loop exists near hA-values of SN1. The isolated envelope has an inner envelope of unstable periodic orbits that terminates at a homoclinic bifurcation (HC2) to the right, but undergoes a saddle-node bifurcation of periodic orbits (SNP) to the left, forming a stable outer envelope. As shown in the inset, this envelope becomes unstable at a period doubling bifurcation (PD) and terminates to the right at another homoclinic bifurcation, denoted HC3.