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Fig. 10 | The Journal of Mathematical Neuroscience

Fig. 10

From: Timescales and Mechanisms of Sigh-Like Bursting and Spiking in Models of Rhythmic Respiratory Neurons

Fig. 10

Mechnisms underlying sigh-like bursting solutions. Simulation of the SB solution generated by (5a)–(5g), together with the bifurcation diagrams. (A) Temporal evolution of v. Yellow symbols mark key points along the solution (star: start of the SB solution as in Fig. 5; triangle: start of the sigh-like burst; circle: start of jumping up of \(ca_{i}\); square: termination of the sigh-like burst). (B) Two-parameter bifurcation diagrams showing LF (blue) and HC (green) curves together with the trajectory from panel (A) in \((na_{i}, ca_{i})\)-space, the enlarged view of the lower left part of which is given by Fig. 5C. (C) The curves of saddle-node bifurcations corresponding to the upper folds of the bursting branch and the spiking branch in Fig. 7, denoted as \(\mathrm{SN}_{1}\) and \(\mathrm{SN}_{2}\), respectively. We use \(\mathrm{SN}_{1}\) (solid red) to approximate the bursting/spiking boundary for the fast-slow subsystem (dashed red) and use \(\mathrm{SN}_{2}\) (solid blue) to approximate the onset of jumping up of \(ca_{i}\) (dashed blue), respectively

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