For citation:
Ivanova A. S., Kuznetsov S. P. On dynamics of model networks composed of logistic maps with inertial and dissipative global coupling. Izvestiya VUZ. Applied Nonlinear Dynamics, 2002, vol. 10, iss. 6, pp. 42-53. DOI: 10.18500/0869-6632-2002-10-6-42-53
On dynamics of model networks composed of logistic maps with inertial and dissipative global coupling
We study a system of globally period-doubling coupled maps, each element interacts with each other. The main attention is given to the domain of the most various and complex behavior, near the onset of chaos. We discuss and compare dynamics of the system with pure inertial and pure dissipative coupling, reveal and illustrate the associated scaling properties.
1. Kaneko K. Clustering, coding, switching, hierarchical ordering, and control in network оf chaotic elements. Physica D. 1990;41(2):137–172. DOI: 10.1016/0167-2789(90)90119-A.
2. Kaneko K. Chaotic but regular Posi-Nega switch among coded attractors by cluster-size variation. Phys. Rev. Lett. 1989;63(3):219–223. DOI: 10.1103/PhysRevLett.63.219.
3. Kuznetsov SP. Universality and scaling in the behavior of coupled Feigenbaum systems. Radiophys. Quantum Electron. 1985;28(8):681–695. DOI: 10.1007/BF01035195.
4. Kook H, Ling FH, Schmidt С. Universal behavior of coupled nonlinear systems. Phys. Rev. А. 1991;43(6):2700–2708. DOI: 10.1103/PhysRevA.43.2700.
5. Кim S-Y, Kook H. Period doubling in coupled maps. Phys. Rev. Е. 1993;48(2):785–799. DOI: 10.1103/PhysRevE.48.785.
6. Feigenbaum MJ. Quantitative universality for a class of nonlinear transformations. J. Stat. Phys. 1978;19(1):25–52. DOI: 10.1007/BF01020332.
7. Kuznetsov SP. Universality and scaling in two-dimensional coupled map lattices. Chaos, Solitons and Fractals. 1992;2(3):281–301. DOI: 10.1016/0960-0779(92)90037-N.
8. Taborov AV, Maistrenko YL, Mosekilde E. Partial synchronization in a system оf coupled logistic mар. International Journal оf Bifurcation and Chaos. 2000;10(5):1051–1066. DOI: 10.1142/S0218127400000748.
9. Kuznetsov AP, Kuznetsov SP. Critical dynamics of coupled-map lattices at onset of chaos (review). Radiophys. Quantum Electron. 1991;34(10–12):845–868. DOI: 10.1007/BF0108361.
10. Feigenbaum MJ. The universal metric properties of nonlinear transformations. J. Stat. Phys. 1979;21(6):669–706. DOI: 10.1007/BF01107909.
11. Kuznetsov SP. Renormalization group, universality and scaling in dynamics of coupled mар lattices. In: Kaneko K. editor. Theory and Applications of Coupled Mар Lattices. John Wiley & Sons Ltd; 1993. P. 50–93.
12. Kim S-Y, Kook H. Renormalization analysis of two coupled maps. Phys. Lett. A. 1993;178(3–4):258–264. DOI: 10.1016/0375-9601(93)91099-Q.
- 457 reads