Bifurcations And Chaos In Piecewise-Smooth Dynamical Systems: Applications To Power Converters, Relay And Pulse-Width Modulated Control Systems, And Human Decision-Making Behavior

Chapter 5: Chaotic Oscillations in Pulse-Width Modulated Systems

5.1 Application of Pulse-Width Modulation in Power Electronics

Pulse modulated systems have a wide range of applications in control engineering, communication, and information technology. Similar types of regulation is also used in many biological control systems. It is well-known, for instance, that the insulin producing pancreatic ?-cells in intact islets of Langerhans display a bursting behavior with alternations between an active (spiking) phase and a silent phase [1, 2, 3, 4]. It is also established [5, 6] that the secretion of insulin depends on the fraction of time that the cells spend in the active state, and that this fraction increases with the concentration of glucose in the extracellular environment. The bursting dynamics controls the influx of Ca +2 ions into the cell, and calcium is an essential trigger for the release of insulin. In this way the bursting dynamics takes part in the control of the glucose concentration in the blood. At glucose concentration below 5 mM, the cells do not burst at all. For high glucose concentrations (>22 mM), on the other hand, the cells spike continuously, and the secretion of insulin saturates [7].

Pulse modulation is also applied in many areas of science where the technique is used, for instance, to stabilize the experimental conditions and minimize the significance of exogenous noise or gradual drift. An example is the X-ray scattering experiments performed by Carlson et al. [8, 9] at IBM Research Center in the early 1970 s on one of the first fully-computerized...

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