Experimental system of coupled map lattices

Abstract

We design an optical feedback loop system consisting of a liquid-crystal spatial light modulator (SLM), a lens, polarizers, a CCD camera, and a computer. The system images every SLM pixel onto one camera pixel. The light intensity on the camera pixel shows a nonlinear relationship with the phase shift applied by the SLM. Every pixel behaves as a nonlinear map, and we can control the interaction of pixels. Therefore, this feedback loop system can be regarded as a spatially extended system. This experimental coupled map has variable dimensions, which can be up to 512 by 512. The system can be used to study high-dimensional problems that computer simulations cannot handle.

Graphical abstract

Keywords

coupled map lattices / photoelectric feedback loop

References

[1] K. Kaneko, Collapse of Tori and Genesis of Chaos in Dissipative Systems, Vol. 33, World Scientific, 1986

[2] K. Kaneko, Lyapunov analysis and information flow in coupled map lattices, Physica D23(1), 436 (1986)

[3] K. Kaneko, Pattern dynamics in spatiotemporal chaos: Pattern selection, diffusion of defect and pattern competition intermittency, Physica D34(1), 1 (1989)

[4] K. Kaneko, Spatiotemporal chaos in one-and twodimensional coupled map lattices, Physica D37(1), 60 (1989)

[5] G. Hu and Z. L. Qu, Controlling spatiotemporal chaos in coupled map lattice systems, Phys. Rev. Lett. 72(1), 68 (1994)

[6] P. M. Gade and C.-K. Hu, Synchronous chaos in coupled map lattices with small-world interactions, Phys. Rev. E62(5), 6409 (2000)

[7] O. N. Björnstad, R. A. Ims, and X. Lambin, Spatial population dynamics: analyzing patterns and processes of population synchrony, Trends in Ecology & Evolution14(11), 427 (1999)

[8] J. Garcia-Ojalvo and R. Roy, Spatiotemporal communication with synchronized optical chaos, Phys. Rev. Lett. 86(22), 5204 (2001)

[9] H. Kantz, A robust method to estimate the maximal Lyapunov exponent of a time series, Phys. Lett. A185(1), 77 (1994)

[10] L. M. Pecora, F. Sorrentino, A. M. Hagerstrom, T. E. Murphy, and R. Roy, Cluster synchronization and isolated desynchronization in complex networks with symmetries, Nature Communications5, 4079 (2014)

[11] S. Liu and M. Zhan, Clustering versus non-clustering phase synchronizations, Chaos24, 013104 (2014)

[12] M. Zhan, S. Liu, and Z. He, Matching rules for collective behaviors on complex networks: Optimal configurations for vibration frequencies of networked harmonic oscillators, PloS ONE8(12), e82161 (2013)

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg