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Example text

2-8). The lower half, y < 0 will be centred around the equilibrium at the origin of the co-ordinates (0, 0). The upper half is centred around an equilibrium with the co-ordinates 0, 1. Like in the linear case there is an exponential change in the sha e of the ellipses which is determined by the logarithmic decrement d = 2nh - h2 and one can therefore determine the so-called sequence function which gives the consecutive points where a phase path intersects the x axis. One finds: J 21 OSCILLATING SYSTEMS Fig.

2-19 for the half line I is: B A e-klct and for half line 11: (2-20) Fig. 2-6. Phase diagram of a thermostatically controlled oven. 61 and 62 are the critical switch on and switch off temperatures. 20 CYCLOSTRATIGRAPHY AND THE MILANKOVITCH THEORY 9 4 Fig. 2-7. The temperature 19 of a thermostatically controlled oven as function of time 1. The system has a single equilibrium I9 = Wo/kwhich is the temperature at which power and heat loss compensate each other. If Wo/k> 01 the oven will heat to the first switch off time and from then on it will operate in a self-oscillating mode.

Predictability can be restored by adding a small periodic force to the process and eq. 2-26 can be written as: (3-19) In this, we is the external forcing frequency which is supposed to have a very small amplitude E . The complex valued coefficients describes the coupling of the forcing with the normal form variable. Nicolis (1985) finds that the system can become stable when it goes into resonance with the forcing function. e. when = 0 and when we = k o e , where k is an integer. This means that the self-oscillatingfrequency must be a harmonic of the forcing frequency.

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