STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.

Structure and Applications of a Rhamnolipid Surfactant Produced in Soybean Oil Waste

Soybean oil soapstock was utilized as an alternative carbon source for the production of rhamnolipids by Pseudomonas aeruginosa LBI strain. The chemical composition and properties of the rhamnolipid mixture obtained were determined to define its potential applications. The chemical characterization of the rhamnolipid has revealed the presence of ten different homologues. The monorhamnolipid RhaC(10)C(10) and the dirhamnolipid Rha(2)C(10)C(10) were the main components of the mixture that showed predominance of 44% and 29%, respectively, after 144-h of cultivation. The biosurfactant was able to form stable emulsions with several hydrocarbons and showed excellent emulsification for soybean oil and chicken fat (100%). The rhamnolipid removed 67% of crude oil present in sand samples and presented antimicrobial activity against Bacillus cereus and Mucor miehei at 64 mu g/mL and inhibition of Neurospora crassa, Staphylococcus aureus, and Micrococcus luteus at 256 mu g/mL. The results demonstrated that the rhamnolipid produced in soybean oil soapstock can be useful in environmental and food industry applications.