Anisotropy-controlled topological stability of discrete vortex solitons in optically induced photonic lattices.

We realize an experimental control over the topological stability of three-lobe discrete vortex solitons by modifying the symmetry of a hexagonal photonic lattice optically induced in a photorefractive crystal. By continuously deforming the lattice wave in one transverse direction, we manipulate the coupling between lattice sites and induce or inhibit the reversal of soliton vorticity.

Observation of multivortex solitons in photonic lattices.

We report on the first observation of topologically stable spatially localized multivortex solitons generated in optically induced hexagonal photonic lattices. We demonstrate that topological stabilization of such nonlinear localized states can be achieved through self-trapping of truncated two-dimensional Bloch waves and confirm our experimental results by numerical simulations of the beam propagation in weakly deformed lattice potentials in anisotropic photorefractive media.

Delay-sustained pattern formation in subexcitable media.

The influence of time-delayed feedback on pattern formation in subexcitable media represented by a net of FitzHugh-Nagumo elements, a minimal model of neuronal dynamics, is studied. Without feedback, wave fronts die out after a short propagation length (subexcitable net dynamics). Applying time-delayed feedback with appropriate feedback parameters, pattern formation is sustained and the wave fronts may propagate through the whole net (signature of excitable behavior). The coherence of noise-induced patterns is significantly enhanced if feedback with appropriately chosen parameters is applied, and shows a resonancelike dependency on the delay time. In a next step, the transition to the excitable regime is investigated in dependence on the quota of elements, which get the feedback signal. It is sufficient to control approximately half of the elements to achieve excitable behavior. Regarding a medical application, where the external control of a neural tissue would affect not single neurons but clusters of neurons, the spatial correlation of the controlled elements is of importance. The selection of the elements, which get the feedback signal, is based on a spatially correlated random distribution. It is shown that the correlation length of this distribution affects the pattern formation.

Doubly diversity-induced resonance.

The influence of variability on the response of a net of bistable FitzHugh-Nagumo elements to a weak signal is investigated. The response of the net undergoes a resonancelike behavior due to additive variability. For an intermediate strength of additive variability the external signal is optimally enhanced in the output of the net (diversity-induced resonance). Furthermore, we show that additive noise strongly influences the diversity-induced resonance. Afterwards the interplay of additive and multiplicative variability on the response of the net is investigated. Starting with asymmetric bistable elements the enhancement of the signal is not very pronounced in the presence of additive variability. Via symmetry restoration by multiplicative variability the resonance is further enhanced. We call this phenomenon doubly diversity-induced resonance, because the interplay of both, additive and multiplicative variability, is essential to achieve the optimal enhancement of the signal. The restoration of symmetry can be explained by a systematic effect of the multiplicative variability, which changes the thresholds for the transitions between the two stable fixed points. We investigate the response to variability for globally and diffusively coupled networks and in dependency on the coupling strength.

Variability-sustained pattern formation in subexcitable media.

Starting with a subexcitable net of FitzHugh-Nagumo elements it is shown that parameter variability (diversity) is able to induce pattern formation. These patterns are most coherent for an intermediate variability strength. This effect is similar to the well-known spatiotemporal stochastic resonance generated by additive noise in subexcitable media. Furthermore, variability is able to induce a transition to an excitable behavior of the net. This transition strongly depends on the coupling strength between the elements and it is found only for strong coupling. For weaker coupling one observes a lifetime lengthening of waves propagating through the medium, but the net stays subexcitable.

Variability-induced transition in a net of neural elements: From oscillatory to excitable behavior.

Starting with an oscillatory net of neural elements, increasing variability induces a phase transition to excitability. This transition is explained by a systematic effect of the variability, which stabilizes the formerly unstable, spatially uniform, temporally constant solution of the net. Multiplicative noise may also influence the net in a systematic way and may thus induce a similar transition. Adding noise into the model, the interplay of noise and variability with respect to the reported transition is investigated. Finally, pattern formation in a diffusively coupled net is studied, because excitability implies the ability of pattern formation and information transmission.

Noise-memory induced excitability and pattern formation in oscillatory neural models.

We report a noise-memory induced phase transition in an array of oscillatory neural systems, which leads to the suppression of synchronous oscillations and restoration of excitable dynamics. This phenomenon is caused by the systematic contributions of temporally correlated parametric noise, i.e., possessing a memory, which stabilizes a deterministically unstable fixed point. Changing the noise correlation time, a reentrant phase transition to noise-induced excitability is observed in a globally coupled array. Since noise-induced excitability implies the restoration of the ability to transmit information, associated spatiotemporal patterns are observed afterwards. Furthermore, an analytic approach to predict the systematic effects of exponentially correlated noise is presented and its results are compared with the simulations.

Counterpropagating dipole-mode vector soliton.

We experimentally observed a counterpropagating dipole-mode vector soliton in a photorefractive SBN:60Ce crystal. We investigated the transient formation dynamics and show that the formation process differs significantly from the copropagating geometry. The experimental results are compared with fully anisotropic numerical simulations and show good qualitative agreement.

Lateral diffusion of CO2 in leaves of the crassulacean acid metabolism plant Kalanchoe daigremontiana Hamet et Perrier.

Dynamic patchiness of photosystem II (PSII) activity in leaves of the crassulacean acid metabolism (CAM) plant Kalanchoe daigremontiana Hamet et Perrier, which was independent of stomatal control and was observed during both the day/night cycle and circadian endogenous oscillations of CAM, was previously explained by lateral CO2 diffusion and CO2 signalling in the leaves [Rascher et al. (2001) Proc Natl Acad Sci USA 98:11801-11805; Rascher and Luttge (2002) Plant Biol 4:671-681]. The aim here was to actually demonstrate the importance of lateral CO2 diffusion and its effects on localized PSII activity. Covering small sections of entire leaves with silicone grease was used for local exclusion of a contribution of atmospheric CO2 to internal CO2 via transport through stomata. A setup for combined measurement of gas exchange and chlorophyll fluorescence imaging was used for recording photosynthetic activity with a spatiotemporal resolution. When remobilization of malic acid from vacuolar storage and its decarboxylation in the CAM cycle caused increasing internal CO2 concentrations sustaining high PSII activity behind closed stomata, PSII activity was also increased in adjacent leaf sections where vacuolar malic acid accumulation was minimal as a result of preventing external CO2 supply due to leaf-surface greasing, and where therefore CO2 could only be supplied by diffusion from the neighbouring malic acid-remobilizing leaf tissue. This demonstrates lateral CO2 diffusion and its effect on local photosynthetic activity.

Incoherent multi-gap optical solitons in nonlinear photonic lattices.

We demonstrate numerically that partially incoherent light can be trapped in the spectral band gaps of a photonic lattice, creating partially incoherent multi-component spatial optical solitons in a self-defocusing nonlinear periodic medium. We find numerically such incoherent multi-gap optical solitons and discuss how to generate them in experiment by interfering incoherent light beams at the input of a nonlinear periodic medium.

Incoherent vector vortex-mode solitons in self-focusing nonlinear media.

We suggest a novel type of composite spatial optical soliton created by a coherent vortex beam guiding a partially incoherent light beam in a self-focusing nonlinear medium. We show that the incoherence of the guided mode may enhance, rather than suppress, the vortex azimuthal instability, and we also demonstrate strong destabilization of dipole-mode solitons by partially incoherent light.

Perturbations of malate accumulation and the endogenous rhythms of gas exchange in the Crassulacean acid metabolism plant Kalanchoë daigremontiana: testing the tonoplast-as-oscillator model.

In continuous light, leaves of the Crassulacean acid metabolism (CAM) plant Kalanchoë daigremontiana Hamet et Perrier exhibit a circadian rhythm of CO2 uptake, stomatal conductance and leaf-internal CO2 pressure. According to a current quantitative model of CAM, the pacemaking mechanism involves periodic turgor-related tension and relaxation of the tonoplast, which determines the direction of the net flux of malate between the vacuole and the cytoplasm. Cytoplasmic malate, in turn, through its inhibitory effect on phospho enolpyruvate carboxylase, controls the rate of CO2 uptake. According to this mechanism, when the accumulation of malate is disrupted by removing CO2 from the ambient air, the induction of a phase delay with respect to an unperturbed control plant is expected. First, using the mathematical model, such phase delays were observed in numerical simulations of three scenarios of CO2 removal: (i) starting at a trough of CO2 uptake, lasting for about half a cycle (ca. 12 h in vivo); (ii) with the identical starting phase, but lasting for 1.5 cycles (ca. 36 h); and (iii) starting while CO2 increases, lasting for half a cycle again. Applying the same protocols to leaves of K. daigremontiana in vivo did not induce the predicted phase shifts, i.e. after the end of the CO2 removal the perturbed rhythm adopted nearly the same phase as that of the control plant. Second, when leaves were exposed to a nitrogen atmosphere for three nights prior to onset of continuous light to prevent malate accumulation, a small, 4-h phase advance was observed instead of a delay, again contrary to the model-based expectations. Hence, vacuolar malic acid accumulation is ruled out as the central pacemaking process. This observation is in line with our earlier suggestion [T.P. Wyka, U. Lüttge (2003) J Exp Bot 54:1471-1479] that in extended continuous light, CO2 uptake switches gradually from a CAM-like to a C3-like mechanism, with oscillations of the two CO2 uptake systems being tightly coordinated. It appears that the circadian rhythm of gas exchange in this CAM plant emerges from one or several devices that are capable of generating temporal information in a robust manner, i.e. they are protected from even severe metabolic perturbations.

Soliton transverse instabilities in anisotropic nonlocal self-focusing media.

We study, both numerically and experimentally, the transverse modulational instability of spatial stripe solitons in anisotropic nonlocal photorefractive media. We demonstrate that the instability scenarios depend strongly on the stripe orientation, but the anisotropy-induced features are largely suppressed for spatial solitons created by self-trapping of partially incoherent light.

Identification of rhythmic subsystems in the circadian cycle of crassulacean acid metabolism under thermoperiodic perturbations.

Leaves of the Crassulacean acid metabolism (CAM) plant Kalanchoë daigremontiana Hamet et Perrier de la Bâthie show overt circadian rhythms in net CO2 uptake, leaf conductance to water and intercellular CO2 concentration, which are entrained by periodic temperature cycles. To probe their sensitivity to thermoperiodic perturbations, intact leaves were exposed to continuous light intensity and temperature cycles with a period of 16 h, applying a set of different baseline temperatures and thermodriver amplitudes. All three overt rhythms were analyzed with respect to their frequency spectra and their phase relations with the thermodriver. For most stimulation protocols, stomatal conductance and net CO2 change were fully or partially entrained by the temperature pulses, while the internal CO2 concentration remained dominated by oscillations in the circadian range. Prolonged time series recorded for up to 22 d in continuous light underline the robustness of these circadian oscillations. This suggests that the overt circadian rhythm of net CO2 uptake in CAM results from the interaction of two coupled original systems: (i) an endogenous cycle of CO2 fixation in the mesophyll, showing very robust periodic activity, and (ii) stomatal movements that respond to environmental stimuli independently of rhythmic processes in the mesophyll, and thus modulate the gas exchange amplitude.

Multicomponent dipole-mode spatial solitons.

We study (2+1) -dimensional multicomponent spatial vector solitons with a nontrivial topological structure of their constituents and demonstrate that these solitary waves exhibit a symmetry-breaking instability, provided their total topological charge is nonzero. We describe a novel type of stable multicomponent dipole-mode solitons with intriguing swinging dynamics.