Unidirectional motion along an annular water channel can be observed in an experiment even with only one camphor disk or boat. Moreover, the collective motion of camphor disks or boats in the water channel exhibits a homogeneous and an inhomogeneous state, depending on the number of disks or boats, which looks like a kind of bifurcation phenomena. In a theoretical research, the unidirectional motion is represented by a traveling wave solution in a model. Hence it suffices to investigate a linearized eigenvalue problem in order to prove the destabilization of a traveling wave solution. However, the eigenvalue problem is too difficult to analyze even if the number of camphor disks or boats is 2. Hence we need to make a reduction on the model. In the present paper, we apply the center manifold theory and reduce the model to an ordinary differential system.
We tested the hypotheses that a reduction of incident light of 50 % over sun-acclimated leaves of water stressed kiwifruit (Actinidia deliciosa var. deliciosa) would (1) reduce stomatal limitations to carbon supply and (2) mitigate the inactivation of the primary photochemistry associated with photosystem (PS) II, thereby this increases carbon gain and water-use efficiency (WUE). Groups of field-grown vines were either shaded or left naturally exposed and subjected to progressive water stress in order to study moderately and severely droughted vines, while other groups were well irrigated. Daily variations in leaf gas exchange and midday chlorophyll (Chl) a fluorescence were determined once plants had -0.6 MPa (moderate stress) and -1.0 MPa pre-down leaf water potential (severe stress). Variations in Chl pigment content and specific leaf area (SLA) are also discussed. Results reveal that 50 % shade application maintained efficiency of PSII close to 0.8 even under severe drought so that to prevent its large decline (0.65) recorded in sunlit leaves. Under moderate stress level stomata behaviour dominated upon metabolic impairments of PSII. Reduction of irradiance increased WUE (15-20 %) in droughted vines, representing a valuable intervention to save photosynthetic apparatus and improve WUE in vines experiencing typical Mediterranean summer stresses. and G. Montanaro, B. Dichio, C. Xiloyannis.