Abstract
In this paper three methods for chaotic synchronization, based on the known linear-nonlinear decomposition method, are proposed. The main advantage of this kind of decomposition is that the stability analysis of the synchronization scheme can be done by a linear error system, so there is no need to calculate the conditional Lyapunov exponents or to design Lyapunov functions. The new aspect of the proposed approaches is, that in contrast to the standard linear-nonlinear decomposition method, strict rules to design the system couplings with many different combinations of additional decomposition of the linear part of the system or with additional feedback coupling are defined
References
- Pecora, L., T. Carroll. Driving systems with chaotic signals. Physical Review A, Vol.44, No.4, 1991, pp.2374- 2384.
- Pecora, L., T. Carroll. Synchronization in chaotic systems. Physical Review Letters, Vol.64, No.8, 1990, pp.821- 824.
- Guemez, J., M. Matias. Modified method for synchronizing and cascading chaotic systems, Physical Review E 52, 1995, pp.2145-2148.
- Pecora, L., T. Carroll, G. Johnson, D. Mar, J. Heagy. Fundamentals of synchronization in chaotic systems, concepts, and applications. Chaos 7(4), 1997, pp.520-543.
- Kocarev, L., U. Parlitz. General approach for chaotic synchronization with applications to communication. Physical Review Letters, Vol.74, No.25, 1995, pp.5028-5031.
- Ogorzalek, M. Taming chaos – part I: Synchronization. IEEE Transactions on Circuits and Systems-I, Vol.40, No.10, 1993, pp.693-699.
- Boccaletti, S., J. Kurths, G. Osipov, D. Valladares, C. Zhou. The synchronization of chaotic systems. Physics Reports 366 (2002), pp.1-101.
- Morgul, O., M. Feki, Synchronization of chaotic systems by using occasional coupling, Physical Review E, Vol.55, No.5, 1997, pp.5004-5010.
- Ali, M., J. Fang. Synchronization of chaos and hyperchaos using linear and nonlinear feedback functions. Physical Review E, Vol.55, No.5, 1997, pp.5285-5290.
- Curran, P., J. Suykens, L. Chua. Absolute stability theory and master-slave synchronization. International Journal Bifurcation and Chaos, Vol.7(12), 1997, pp. 2891-2896.
- Suykens, J., A. Vanderwalle. Master-Slave synchronization of Lur’e systems. International Journal Bifurcation and Chaos, Vol.7(3), 1997, pp. 665-669.
- Yu, H., L. Yanzhu. Chaotic synchronization based on stability criterion of linear systems. Physics Letters A, Vol. 314, Issue 4, 2003, pp.292-298.
- Shimizu, T., N. Morioka, On the bifurcation of symmetric limit cycle to an asymmetric one in a simple model, Physics Letters 76A, 1980, pp.201-204.
- Guemez, J., C. Martin. On the behaviour of coupled chaotic systems exhibiting marginal synchronization. Physics Letters A Vol.226, 1997, pp.264-268.
Abstract
In this paper three methods for chaotic synchronization, based on the known linear-nonlinear decomposition method, are proposed. The main advantage of this kind of decomposition is that the stability analysis of the synchronization scheme can be done by a linear error system, so there is no need to calculate the conditional Lyapunov exponents or to design Lyapunov functions. The new aspect of the proposed approaches is, that in contrast to the standard linear-nonlinear decomposition method, strict rules to design the system couplings with many different combinations of additional decomposition of the linear part of the system or with additional feedback coupling are defined
References
- Pecora, L., T. Carroll. Driving systems with chaotic signals. Physical Review A, Vol.44, No.4, 1991, pp.2374- 2384.
- Pecora, L., T. Carroll. Synchronization in chaotic systems. Physical Review Letters, Vol.64, No.8, 1990, pp.821- 824.
- Guemez, J., M. Matias. Modified method for synchronizing and cascading chaotic systems, Physical Review E 52, 1995, pp.2145-2148.
- Pecora, L., T. Carroll, G. Johnson, D. Mar, J. Heagy. Fundamentals of synchronization in chaotic systems, concepts, and applications. Chaos 7(4), 1997, pp.520-543.
- Kocarev, L., U. Parlitz. General approach for chaotic synchronization with applications to communication. Physical Review Letters, Vol.74, No.25, 1995, pp.5028-5031.
- Ogorzalek, M. Taming chaos – part I: Synchronization. IEEE Transactions on Circuits and Systems-I, Vol.40, No.10, 1993, pp.693-699.
- Boccaletti, S., J. Kurths, G. Osipov, D. Valladares, C. Zhou. The synchronization of chaotic systems. Physics Reports 366 (2002), pp.1-101.
- Morgul, O., M. Feki, Synchronization of chaotic systems by using occasional coupling, Physical Review E, Vol.55, No.5, 1997, pp.5004-5010.
- Ali, M., J. Fang. Synchronization of chaos and hyperchaos using linear and nonlinear feedback functions. Physical Review E, Vol.55, No.5, 1997, pp.5285-5290.
- Curran, P., J. Suykens, L. Chua. Absolute stability theory and master-slave synchronization. International Journal Bifurcation and Chaos, Vol.7(12), 1997, pp. 2891-2896.
- Suykens, J., A. Vanderwalle. Master-Slave synchronization of Lur’e systems. International Journal Bifurcation and Chaos, Vol.7(3), 1997, pp. 665-669.
- Yu, H., L. Yanzhu. Chaotic synchronization based on stability criterion of linear systems. Physics Letters A, Vol. 314, Issue 4, 2003, pp.292-298.
- Shimizu, T., N. Morioka, On the bifurcation of symmetric limit cycle to an asymmetric one in a simple model, Physics Letters 76A, 1980, pp.201-204.
- Guemez, J., C. Martin. On the behaviour of coupled chaotic systems exhibiting marginal synchronization. Physics Letters A Vol.226, 1997, pp.264-268.
Details
| Primary Language | English |
|---|---|
| Subjects | Structural Biology |
| Other ID | JA55ZK57CS |
| Journal Section | Articles |
| Authors | |
| Publication Date | August 5, 2016 |
| Published in Issue | Year 2009 Volume: 10 Issue: 2 |