Scaling of Saddle-Node Bifurcations: Degeneracies and Rapid Quantitative Changes

The scaling of the time delay near a "bottleneck" of a generic saddle-node bifurcation is well-known to be given by an inverse square-root law. We extend the analysis to several non-generic cases for smooth vector fields. We proceed to investigate $C^0$ vector fields. Our main result is a new phenomenon in two-parameter families having a saddle-node bifurcation upon changing the first parameter. We find distinct scalings for different values of the second parameter ranging from power laws with exponents in (0,1) to scalings given by O(1). We illustrate this rapid quantitative change of the scaling law by a an overdamped pendulum with varying length.Comment: preprint version - for final version see journal referenc

Flat Peach SUBLOR and SUBLIM and Flat Nectarine PERLA Series

Flat peach and flat nectarine (Prunus persica L. Batsch.) production in Spain started from local cultivars at marginal sites, mainly in the Ebro Valley and Murcia regions. At the end of the 1990s, the introduction of improved cultivars from France and Italy, with more red skin color coverage and better regular shape, fruit size, and stylar cavity closure, together with superior handling and transport conditions led the Spanish peach sector to develop this fruit type on a commercial scale. Currently, Spain is the largest European producer and exporter of flat peach and nectarine, offering a wide range of cultivars covering the producing period from May to September. In 2020, a total of 10.200 ha for flat peach and 481 ha for flat nectarine together produced 263.651 t (20% of the total peach production) (MAPAMA, 2022). To guarantee adaptation to local growing conditions (Font i Forcada et al., 2021a), several national breeding programs started to develop new flat peach and flat nectarine cultivars. One of these breeding programs is the ASF-IRTA breeding program, which is located at Gimenells (Lleida) in the Ebro Valley (northeastern Spain), which is a major region of peach production in Spain (Batlle et al., 2012; Cantín et al., 2017). It was started in 2004, with the objective of developing new cultivars adapted to chilling between 1000 and 1500 chill units or between 42 and 75 chill portions and warm conditions similar to the Mediterranean area (32 °C mean daily summer temperature and 300–400 mm of annual rainfall). It aimed to produce high-quality fruits, both at harvest and after cold storage, with the ultimate goal of satisfying consumers (Font i Forcada et al., 2021a, 2021b). As a result of this collaborative effort, the ASF-IRTA scion peach breeding program has already released the SUBLOR (one flat yellow-fleshed peach), SUBLIM (six flat white-fleshed peach), and PERLA (two flat white-fleshed nectarine) series. These nine new flat peach and nectarine cultivars produce highly attractive yellow-fleshed or white-fleshed fruits with high coverage of red skin, a balanced or acid flavor, sweet taste, and good flesh firmness. The harvesting calendar of these series will be progressively completed with new future releases.info:eu-repo/semantics/publishedVersio

TERRAM and LUX Series: Four Yellow-fleshed and Three White-fleshed Peaches

In Spain, peach [Prunus persica (L.) Batsch] production has experienced an increase of ≈30% during the past 20 years [Ministry of Agriculture, Food and Environment (MAPAMA), 2021]. In 2018, the total peach cultivated surface area was ≈50,000 ha, with the majority of peach production located in Ebro Valley, northeastern Spain. Aragon and Catalonia are the two most important Spanish peach regions within Ebro Valley, producing ≈430,000 and 409,000 tons annually, respectively (MAPAMA, 2021). Spain is the leading European peach producer and the world’s largest exporter, with a crop value of almost USD 1 billion.info:eu-repo/semantics/publishedVersio

MAGNA and BLANQ Series: Two Yellow-fleshed and Three White-fleshed Nectarines

The continuous release of new nectarine [Prunus persica (L.) Batsch] cultivars by breeders from around the world, together with consistent improvements in orchard management strategies by growers, commercial interest in the production of fruit fresh consumption, and the introduction of new cultivars from Spanish scion nectarine breeding programs have positioned Spain as the preeminent worldwide nectarine exporter and currently the largest European producer [Ministry of Agriculture, Food and Environment (MAPAMA), 2021]. In Spain, the main nectarine-producing area is the Ebro Valley that accounts for more than 60% of the total Spanish peach and nectarine production (MAPAMA, 2021).info:eu-repo/semantics/publishedVersio

TERRAM and LUX series : Four yellow-fleshed and three white-fleshed peaches

Altres ajuts: CERCA Programme/Generalitat de Cataluny

MAGNA and BLANQ series : Two yellow-fleshed and three white-fleshed nectarines

Altres ajuts: CERCA Programme/Generalitat de Cataluny