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Comment
. 2011 Jul;138(1):13-9.
doi: 10.1085/jgp.201110668.

Dynamical systems theory in physiology

Arthur Sherman  1
Affiliations
Comment

Dynamical systems theory in physiology

Arthur Sherman. J Gen Physiol. 2011 Jul.
No abstract available

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Figures

Figure 1.
Figure 1.
Linear oscillations. Sinusoidal solutions of (1) for a pendulum with friction (b < 0), negative friction (b > 0), and no friction (b = 0). In the last case, amplitude is constant but depends on the initial velocity of the pendulum. The dashed blue curve is started at the same position but with twice the velocity as the solid black curve.
Figure 2.
Figure 2.
Bifurcation diagrams and time simulations of bursting. Each panel is made with a simplified Chay–Keizer model (Tsaneva-Atanasova et al., 2010). Bifurcation diagrams with overlaid burst trajectories (blue) in upper subpanel. Solid lines, stable solutions; dashed lines, unstable equilibria; dotted line, unstable oscillations. (A) Pure square wave without spikes. (B) β cell–like square-wave bursting. (C) Pituitary-like bursting. (D) Bursting without bistability requires a second slow variable, as in this caricature of bursting in the R15 neuron of Aplysia.
See this image and copyright information in PMC

Comment on

References

    1. Atwater I., Dawson C.M., Scott A., Eddlestone G., Rojas E. 1980. The nature of the oscillatory behavior in electrical activity for the pancreatic β-cell. Biochemistry and Biophysics of the Pancreatic β-cell. G. Thieme, editor; Springer-Verlag, New York: 100–107
    1. Bertram R., Butte M.J., Kiemel T., Sherman A. 1995. Topological and phenomenological classification of bursting oscillations. Bull. Math. Biol. 57:413–439 - PubMed
    1. Cha C.Y., Nakamura Y., Himeno Y., Wang J., Fujimoto S., Inagaki N., Earm Y.E., Noma A. 2011a. Ionic mechanisms and Ca2+ dynamics underlying the glucose response of pancreatic β cells: a simulation study. J. Gen. Physiol. 138:21–37 - PMC - PubMed
    1. Cha C.Y., Santos E., Amano A., Shimayoshi T., Noma A. 2011b. Time-dependent changes in membrane excitability during glucose-induced bursting activity in pancreatic β cells. J. Gen. Physiol. 138:39–47 - PMC - PubMed
    1. Chay T.R. 1990. Bursting excitable cell models by a slow Ca2+ current. J. Theor. Biol. 142:305–315 10.1016/S0022-5193(05)80555-7 - DOI - PubMed

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