Synchronization and peak-to-peak dynamics in networks of low-dimensional chaotic oscillators

International Journal of Bifurcation and Chaos

Volumn 16, Issue 12, 2006, Pages 3631-3642

  Maggi, Stefano ^a   Rinaldi, Sergio ^b  

^a POLITECNICO DI MILANO   (Italy)

^b INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS   (Austria)

Author keywords

Chaotic oscillators; Coherence; Coupling; Networks; Peak to peak dynamics; Synchronization

Indexed keywords

COMPUTER SIMULATION; ELECTRIC NETWORK ANALYSIS; SYNCHRONIZATION; SYSTEMS ANALYSIS;

CHAOTIC OSCILLATORS; COUPLING STRENGTH; DYNAMICAL SYSTEMS; FOOD CHAINS;

OSCILLATORS (ELECTRONIC);

EID: 33847336004     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127406017026     Document Type: Article

References (22)

1. Balmforth, N., Pasquero, C. & Provenzale, A. [2000] "The Lorenz-Fermi-Pasta-Ulam experiment," Physica D 138, 1-43.
2. Blasius, B., Huppert, L. & Stone, L. [1999] "Complex dynamics and phase synchronization in spatially extended ecological systems," Nature 399, 354-359.
3. Blasius, B. & Stone, L. [2000] "Chaos and phase synchronization in ecological systems," Int. J. Bifurcation and Chaos 10, 2361-2380.
4. Boccaletti, S., Kurths, J., Osipov, G., Valladares, D. L. & Zhou, C. S. [2002] "The synchronization of chaotic systems," Phys. Rep. 366, 1-101.
5. Candaten, M. & Rinaldi, S. [2000] "Peak-to-peak dynamics: A critical survey," Int. J. Bifurcation and Chaos 10, 1805-1819.
6. Candaten, M. & Rinaldi, S. [2003] "Peak-to-peak dynamics in food chain models," Theoret. Popul. Biol. 63, 257-267.
7. Elton, C. & Nicholson, M. [1942] "The ten-year cycle in numbers of the lynx in Canada," J. Anim. Ecol. 11, 215-244.
8. Hastings, A. & Powell, T. [1991] "Chaos in a three-species food chain," Ecol. 72, 896-903.
9. King, A. A. & Schaffer, W. M. [2001] "The geometry of a population cycle: A mechanistic model of the snow-shoe hare cycle," Ecol. 82, 814-830.
10. Kuznetsov, Y. A. & Rinaldi, S. [1996] "Remarks on food chain dynamics," Math. Biosci. 134, 1-33.
11. Kuznetsov, Y. A., Feo, O. D. & Rinaldi, S. [2001] "Belyakov homoclinic bifurcations in a tritrophic food chain model," SIAM J. Appl. Math. 62, 462-487.
12. Liu, Z. & Lai, Y.-C. [2001] "Coherence resonance in coupled chaotic oscillators," Phys. Rev. Lett. 86, 4737-4740.
13. Lorenz, E. N. [1963] "Deterministic nonperiodic flow," J. Atmosph. Sci. 20, 130-141.
14. Manrubia, S. C., Mikhailov, A. S. & Zanette, D. H. [2004] Emergence of Dynamical Order - Synchronization Phenomena in Complex Systems (World Scientific, Singapore).
15. Okubo, A. [1980] Diffusion and Ecological Problems: Mathematical Models (Springer-Verlag).
16. Pecora, L. M. & Carrol, T. L. [1990] "Synchronization in chaotic systems," Phys. Rev. Lett. 64, 821-824.
17. Pecora, L. M. & Carroll, T. L. [1998] "Master stability functions for synchronized coupled systems," Phys. Rev. Lett. 80, 2109-2112.
18. Pikovsky, A., Rosenblum, M. & Kurths, J. [2001] Synchronization - A Universal Concept in Nonlinear Sciences (Cambridge University Press).
19. Pivka, L., Wu, C. W. & Huang, A. [1996] "Lorenz equation and Chua's equations," Int. J. Bifurcation and Chaos 6, 2443-2489.
20. Rinaldi, S., Candaten, M. & Casagrandi, R. [2001] "Evidence of peak-to-peak dynamics in ecology," Ecol. Lett. 4, 610-617.
21. Rosenzweig, M. L. & MacArthur, R. H. [1963] "Graphical representation and stability conditions of predator-prey interactions," Amer. Naturalist 97, 209-223.
22. Rössler, O. E. [1976] "An equation for continuous chaos," Phys. Lett. A 57, 397-398.