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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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(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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(10) 
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