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2.6 Stability Theory 57

Figure 2.6.7: Van der Pol oscillator: (a) time history; (b) phase plane

See Figure 2.6.8 for illustration of the behavior of the state vector.

Note that stability and asymptotic stability are local concepts in the
sense that, if the initial perturbation is too large, the subsequent states
x(t) may stray arbitrarily far from x e . There exists, therefore, a region

Copyright © 2004 by Marcel Dekker, Inc.