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

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