Due to universality following from the renormalization group approach, spatial-temporal dynamics between order and chaos in coupled map lattices should be intrinsic to a class of spatially extended systems built of cells represented by dissipative period-doubling systems of any nature. Here we consider several examples of physical systems studied in real experiments.

As known after Linsay [1981], a periodically driven circuit composed of inductance, resistor, and p-n junction demonstrates the period-doubling transition to chaos in accordance with the Feigenbaum scenario. In a system of two coupled circuits of this kind one has to expect the dynamical behavior of the same type as in two coupled logistic maps.

In the following figure we show a schema studied in an experimental work of B.P.Bezruchko and co-authors [V.V.Astakhov, B.P.Bezruchko et al. Sov.Tech.Phys.Lett.14, No 1 (1988)].

In the parameter region of periodic dynamics of cells, say 2, 4, 8 (in units of the period of external driving) multistability is observed in the experiment of the same nature as in coupled logistic maps, associated with a possibility of a phase shift of oscillations in both cells. The next figure shows phase portraits for different regimes of period 4. Left-hand pictures are photos from oscilloscope screen, and the right=hand ones are the corresponding portraits for coupled logistic maps.

Charts of dynamical regimes obtained in the experiment (see the figures below) look in the same manner as for two logistic maps with dissipative coupling.

One special point is presence of quasiperiodic regime on an anti-phase sheet between regimes of minimal period and that of doubled period. This behavior was explained theoretically in the paper [E.N.Erastova, S.P.Kuznetsov. Sov. Phys. Tech. Phys., 36, No 2, (1991)]

The first picture shows experimental spectrum of oscillations, and the second one presents voltages in two circuits versus time.

The next figure presents a schema studied in experiment [V.V.Astakhov, B.P.Bezruchko, V.I.Ponomarenko, E.P.Seleznev, 10-th school-conference on microwave electronics and radiophysics, Saratov, 1996] that is a chain of six RL-diode circuits driven by periodic external oscillator, with periodic boundary conditions. It is worth noting that careful adjustment has been performed to have as far as possible identical cells and ensure the translation invariance.

Multistability was observed in the system and a variety of regimes with different spatial domain structures. In the following picture a schema is shown from the cited work that explains structure and genetic connections of the observed regimes. .

The picture shows schema of electronic delay feedback oscillator studied experimentally in the work [B.P.Bezruchko, V.Yu. Kamenskii et al. Sov.Tech.Phys.Lett., vol.14, No 6, p.448 (1988)]. As delay line a device was used composed of analog-digital transformer, digital delay microchip, and digital-analog transformer. Nonlinear element characteristic corresponded to a unimodal map with quadratic extremum. Filter was composed of a chain of linear inertial elements of the first order and ensured a transfer characteristic of approximately Gaussian form. The dynamical equation is

Let we consider voltage U_n as function of time and subdivide the time axis over fragments of duration T=T₀+DT, where DT is contribution of the filter chain to the full delay time. Now we may interpret time inside each fragment as spatial coordinate in some medium, and numbers of the fragments as discrete time. Due to structure of the schema under consideration and to symmetry of the Gaussian transfer function this will be the coupled map medium with symmetric dissipative (diffusive) coupling.

Oscilloscope pictures obtained in the experiment qualitatively well correspond to patterns observed in numerical computations for the lattice of dissipatively coupled maps.

Chart of regimes in the parameter plane is also in good correspondence with that discussed earlier in the section devoted to finite-size scaling (in the present case analog of the system size is the delay time T).