Global synchronization of coupled delayed neural networks and applications to chaotic CNN models. (English) Zbl 1077.37506

Summary: This paper formulates the model and then studies its dynamics of a system of linearly and diffusively coupled identical delayed neural networks (DNNs), which is a generalization of delayed Hopfied neural networks (DHNNs) and delayed cellular neural networks (DCNNs). In particularly, a simple yet generic sufficient condition for global synchronization of such coupled DNNs is derived based on the Lyapunov functional methods and Hermitian matrix theory. It is shown that global synchronization of coupled DNNs is ensured by a suitable design of the coupling matrix and the inner linking matrix. Furthermore, the result is applied to some typical chaotic neural networks. Finally, numerical simulations are presented to demonstrate the effectiveness of the approach.


37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
Full Text: DOI


[1] Cao J., Phys. Lett. 270 pp 157–
[2] DOI: 10.1142/9789812798640
[3] Chen Y., Matrix Analysis (2000)
[4] Fire P., Science 291 pp 1560–
[5] DOI: 10.1007/978-1-4612-9892-2
[6] DOI: 10.1073/pnas.91.1.63
[7] DOI: 10.1016/S0960-0779(02)00214-X · Zbl 1065.70015
[8] Lu H., IEEE Trans. Circuits Syst. 43 pp 700–
[9] Lu H., Phys. Rev. 64 pp 1–
[10] Lu H., Phys. Lett. 298 pp 109– · Zbl 0995.92004
[11] DOI: 10.1063/1.166278 · Zbl 0933.37030
[12] Pecora L. M., Phys. Rev. 58 pp 347–
[13] DOI: 10.1103/PhysRevLett.80.2109
[14] DOI: 10.1109/81.904879 · Zbl 0994.82065
[15] Rangarajan G., Phys. Lett. 296 pp 312–
[16] Ruan J., Neural Dynamical Models, Methods and Application (2002)
[17] DOI: 10.1017/S0140525X00047336
[18] DOI: 10.1038/35004588
[19] DOI: 10.1109/81.974874 · Zbl 1368.93576
[20] DOI: 10.1142/S0218127402004292
[21] Wu C. W., IEEE Trans. Circuits Syst. 42 pp 430–
[22] DOI: 10.1109/81.983875 · Zbl 1368.93616
[23] Zhou T., Phys. Lett. 301 pp 231– · Zbl 0997.37015
[24] DOI: 10.1109/81.222797 · Zbl 0782.92003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.