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This system of differential equations (DE1) has two eigenvalues of opposite sign (λ=1 and λ=−2). The point (0,0) is unstable and called a saddle point.

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 (1)

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 (2)

This system of differential equations (DE2) has two eigenvalues of opposite sign (λ=1 and λ=−1). The point (0,0) is unstable and called a saddle point.

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 (3)

This system of differential equations (DE3) has two negative eigenvalues (λ=−1 and λ=−4). The point (0,0) is called a sink or a stable node.

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 (4)

This system of differential equations (DE4) has two positive eigenvalues (λ=1 and λ=4). The point (0,0) is called a source or an unstable node.

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 (5)

This system of differential equations (DE5) has two complex conjugate eigenvalues (λ= ±) with a negative real part. The point (0,0) is called a stable spiral.

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 (7)

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 (8)

This system of differential equations (DE6) has two complex conjugate eigenvalues (λ= ±) with a positive real part. The point (0,0) is called an unstable spiral.

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 (9)

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 (10)

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