11.2 Stability of Linear Systems
INTRODUCTION
We have seen that the plane autonomous system
gives rise to a vector field V(x, y) = (P(x, y), Q(x, y)), and a solution X = X(t) of the system may be interpreted as the resulting path of a particle that is initially placed at position X(0) = X0. If X0 is a critical point of the system, then the particle remains stationary. In this section we examine the behavior of solutions when X0 is chosen close to a critical point of the system.
Some Fundamental Questions
Suppose that X1 is a critical point ...
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