Topic 14.6: Stiff Differential Equations (Engineering Application)

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The circuit

Figure 1. Negative resistance oscillatory circuit.

where the highlighted resistor has negative resistance (e.g., a tunnel diode) may be described by a differential equation of the form

y⁽²⁾(t) − α(1 − y(t)²) y⁽¹⁾(t) + y(t) = 0

This second-order differential equation exhibits stiff behaviour for large positive values of α. When α = 0, it is a simple oscillatory circuit and harmonic motion.

Reference: Van der Pol Oscillators