Analysis and Control of Complex Dynamical Systems by Kazuyuki Aihara Jun-ichi Imura & Tetsushi Ueta
Author:Kazuyuki Aihara, Jun-ichi Imura & Tetsushi Ueta
Language: eng
Format: epub
Publisher: Springer Japan, Tokyo
Therefore, the system (8.4) has all possible solutions of the logistic map as the synchronization solutions although those solutions may be unstable. Using the solutions of the logistic map, we represent a synchronization fixed point as follows:
The stability of the fixed point is determined by the eigenvalues of a Jacobian matrix of the system. The Jacobian matrix at the fixed point is represented as follows:
where . The Jacobian matrix has a real eigenvalue and a conjugate pair of complex eigenvalues:
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