Replication of Chaos in Neural Networks, Economics and Physics by Marat Akhmet & Mehmet Onur Fen

Author:Marat Akhmet & Mehmet Onur Fen
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

Now, let us check that the conditions of the last theorem are true for the system (6.7.47). The matrix of coefficients of the system (6.7.47) with the assumed coefficients is .

The eigenvalues of the matrix A are where and . The real Jordan form of the matrix A is given by and the identity is satisfied where and Evaluating the exponential matrix we have

(6.7.54)

Denote by the matrix norm which is induced by the usual Euclidean norm in . That is,

for any matrix with real entries, and denotes the transpose of the matrix [137].

One can see that

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