Symbolic dynamics generated by a hybrid chaotic systems

We consider piecewise defined differential dynamical systems which can be analysed through symbolic dynamics and transition matrices. We have a continuous regime, where the time flow is characterized by an ordinary differential equation (ODE) which has explicit solutions, and the singular regime, where the time flow is characterized by an appropriate transformation. The symbolic codification is given through the association of a symbol for each distinct regular system and singular system. The transition matrices are then determined as linear approximations to the symbolic dynamics. We analyse the dependence on initial conditions, parameter variation and the occurrence of global strange attractors.

Effects of culture conditions on larval growth and survival of stalked barnacles (Pollicipes pollicipes).

Pollicipes pollicipes (Crustacea: Scalpelliformes) is a highly prized food in Portugal and Spain and con- sequently a species of considerable interest to aqua- culture. Surprisingly, however, larval culture conditions for this barnacle have not been opti- mized. This study investigated the effects of temper- ature, diet, photoperiod and salinity on the growth and survival of P. pollicipes larvae. Temperature had a significant effect on specific growth rate (2.6–5.9% total width per day, from 11 to 24°C), reducing mean development time to the cyprid from 25 days at 11 °C to 10 days at 24°C, although this was accompanied by a significant increase in mortality to over 90% above 22°C. Mid- range temperatures (15–20°C) maximized total survival (19–31% respectively). Algal diets of Tetra- selmis suecica, T. suecica/Skeletonema marinoi and S. marinoi/Isochrysis galbana did not affect specific growth rate significantly, but survival (on average 39% in 15 days) and the proportion of high-quality healthy cyprids was significantly higher on the lat- ter two diets (11–15% of initial number of larvae). Photoperiod did not significantly affect the survival, although specific growth rate was significantly higher at 24:0 and 16:8 L:D. Salinity (20– 40 g L 1 range) did not affect growth and survival significantly. The best growth and survival were accomplished using rearing temperatures of 15–20°C, daily feeding with T. suecica/S. marinoi or I. galbana/S. marinoi and a photoperiod of 24:0 L:D.