The critical point is at (3, 1). It has repeated eigenvalues equal to -1. Hence, there is only one linearly independent eigenvector. Therefore, the critical point at (3, 1) is an asymptotically stable improper node. Fig. 2.3 Asymptotically stable improper node. The critical is (3,1). Case 3: real eigenvalues and both positive The unstable equilibrium point is called a node source. D.E. coefficients k11 k12 k13 / k21 k23 k23 3.00 1.00 0.00 1.00 3.00 0.00 Eigenvalues b = 2 0 0 4 Eigenfunction a = -0.7071 0.7071 0.7071 0.7071
The critical point is at (3, 1). It has repeated eigenvalues equal to -1. Hence, there is only one linearly independent eigenvector. Therefore, the critical point at (3, 1) is an asymptotically stable improper node. Fig. 2.3 Asymptotically stable improper node. The critical is (3,1). Case 3: real eigenvalues and both positive The unstable equilibrium point is called a node source. D.E. coefficients k11 k12 k13 / k21 k23 k23 3.00 1.00 0.00 1.00 3.00 0.00 Eigenvalues b = 2 0 0 4 Eigenfunction a = -0.7071 0.7071 0.7071 0.7071
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