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The behaviour of a linear autonomous system around a critical point is a node if the following conditions are satisfied:

Each path converges to the or away from the critical point (dependent of the underlying equation) as ${\displaystyle t\rightarrow \infty }$ (or as ${\displaystyle t\rightarrow -\infty }$). Furthermore, each path approaches the point asymptotically through a line.

References

1. George F. Simmons, Differential equations with applications and historical notes, Second edition, pp. 447–448.

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