Discuss the critical points in (10)?(13) of Sec. 4.3 by using Tables 4.1 and 4.2.

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Table 4.1 Eigenvalue Criteria for Critical Points (Derivation after Table 4.2) Name (a) Node (b) Saddle point (c) Center (d) Spiral point p = λ₁ + λ₂ q = λ₁λ₂ A = (λ₁ - ₂)² Comments on A₁, A₂ A≥0 P = 0 P# 0 9>0 9 <0 9>0 A <0 Real, same sign Real, opposite signs Pure imaginary Complex, not pure imaginary Table 4.2 Stability Criteria for Critical Points Type of Stability (a) Stable and attractive (b) Stable (c) Unstable p = λ + kg P <0 P≤ 0 P>0 OR q = ληλη 9>0 9>0 9 <0