The chaotic synchronization of third-order systems and second-order driven oscillator is studied in this paper. Such a problem is related to synchronization of strictly different chaotic systems. We show that dynamical evolution of second-order driven oscillators can be synchronized with the canonical projection of a third-order chaotic system. In this sense, it is said that synchronization is achieved in reduced order. Duffing equation is chosen as slave system whereas Chua oscillator is defined as master system. The synchronization scheme has nonlinear feedback structure. The reduced-order synchronization is attained in a practical sense, i.e., the difference e=x(3)-x(1)(') is close to zero for all time t> or =t(0)> or =0, where t(0) denotes the time of the control activation.

In this paper, we present a class of 3-D unstable dissipative systems, which are stable in two components but unstable in the other one. This class of systems is motivated by whirls, comprised of switching subsystems, which yield strange attractors from the combination of two unstable “one-spiral” trajectories by means of a switching rule. Each one of these trajectories moves around two hyperbolic saddle equilibrium points. Both theoretical and numerical results are provided for verification and demonstration.

Lipases and esterases are biocatalysts used at the laboratory and industrial level. To obtain the maximum yield in a bioprocess, it is important to measure key variables, such as enzymatic activity. The conventional method for monitoring hydrolytic activity is to take out a sample from the bioreactor to be analyzed off-line at the laboratory. The disadvantage of this approach is the long time required to recover the information from the process, hindering the possibility to develop control systems. New strategies to monitor lipase/esterase activity are necessary. In this context and in the first approach, we proposed a lab-made sequential injection analysis system to analyze off-line samples from shake flasks. Lipase/esterase activity was determined using p-nitrophenyl butyrate as the substrate. The sequential injection analysis allowed us to measure the hydrolytic activity from a sample without dilution in a linear range from 0.05–1.60 U/mL, with the capability to reach sample dilutions up to 1000 times, a sampling frequency of five samples/h, with a kinetic reaction of 5 min and a relative standard deviation of 8.75%. The results are promising to monitor lipase/esterase activity in real time, in which optimization and control strategies can be designed.

The dynamical behaviour for a generic two-dimensional model of a continuous bioreactor is studied in this article. The state variables for the bio-reacting system are restricted to concentrations of substrate and biomass, where the specific growth rate is a smooth function of the substrate concentration, which can be a kinetic function, monotone or non-monotone (as Monod, Haldane, Teissier, etc.). The effect of input (dilution rate) on multiplicity and bifurcation of equilibrium is shown in open-loop configuration. The absence of limit cycles on open-loop configuration and through state-feedback on the dilution rate are demonstrated. The aim of analysing oscillations under state feedback control is related to the possible improvement of reactor yields under this operation regime. An example for a cell-producing bioreactor illustrates the analytical results.