Linear dynamical system Totally Explained

Everything about Linear Dynamical System totally explained

In a linear dynamical system, the variation of a state vector(an

N

-dimensional vector denoted

mathbf

Note also that

Delta=lambda_1lambda_2

and

au=lambda_1+lambda_2

. Thus if

Delta<0

then the eigenvalues are of opposite sign, and the fixed point is a saddle. If

Delta>0

then the eigenvalues are of the same sign. Therefore if

au>0

both are positive and the point is unstable, and if

au<0

then both are negative and the point is stable. The discriminant will tell you if the point is nodal or spiral (for example if the eigenvalues are real or complex).

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