Certain deterministic non-linear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows for construction of more realistic and better models and thus improved predictive capabilities. This paper describes key features of chaotic systems including strange attractors and Lyapunov exponents. The emphasis is on state space reconstruction techniques that are used to estimate these properties, given scalar observations. Data generated from equations known to display chaotic behaviour are used for illustration. A compilation of applications to real data from widely different fields is given. If chaos is found to be present, one may proceed to build non-linear models, which is the topic of the second paper in this series

This paper is the second in a series of two, and describes the current state of the art in modeling and prediction of chaotic time series. Sample data from deterministic non-linear systems may look stochastic when analysed with linear methods. However, the deterministic structure may be uncovered and non-linear models constructed that allow improved prediction. We give the background for such methods from a geometrical point of view, and briefly describe the following types of methods: global polynomials, local polynomials, multilayer perceptrons and semi-local methods including radial basis functions. Some illustrative examples from known chaotic systems are presented, emphasising the increase in prediction error with time. We compare some of the algorithms with respect to prediction accuracy and storage requirements, and list applications of these methods to real data from widely different areas

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It has previously been shown that guinea pig hepatocytes metabolise morphine in a fashion similar to humans. The metabolism of morphine (5 pM) and the formation of metabolites morphine-3-glucuronide, morphine-6-glucuronide and normorphine was studied in the absence and presence of ethanol (5, 10, 25, 60 and 100 mM) in freshly isolated guinea pig hepatocytes. In order to gain more detailed information, a mathematical model was estimated on experimental data and used to analyse the effects of ehtanol on the reaction rates of the different morphine metabolites. Ethanol inhibited the rate of morphine elimination in a dose-related manner, at the high ethanol concentrations the elimination rate was 40 per cent of the control rate. The formation of morhine-glucuronides was influenced in a biphasic manner. Five and 10 mM ethanol increased both the morphine-3-glucuronide and morphine-6-glucuronide levels after 60 min incubation compared to the control, whereas at the higher ethanol concentrations (25-100 mM) the levels of morphineglucuronides were reduced. Data from the mathematical model, however, demonstrated that the reaction rates for morphine-glucuronide formation were decreased at all ethanol concentrations and in a dose-dependent manner, the interpretation of this-being that at the lower (5 and 10 mM) ethanol concentraions employed in this study, other metabolic pathways of morphine are more heavily inhibited than the glucuronidations, resulting in a shunting towards morphine-3-glucuronide and morphine-6-glucuronide. The pharmacodynamic consequences of these pharmacokinetic effects are thus somewhat diffucult to predict since morphine-6-glucuronide has a higher agonist potency than morphine. At high concentrations ethanol inhibition of morphine metabolism will increase the concentration of morphine and subsequently the euphoric and the toxic effects. The lower quantities of morphine-6-glucuronide formed in the presence of high ethanol concentrations on the other hand most probably imply reduction of such effects and the net pharmacodynamic effect would be uncertain. At low ethanol concentrations, however, morphine-6-glucuronide concentrations increased and morphine metabolism was less inhibited leading to a possible potentiation of the effects of morphine. Thus, a low ehtanol concentration might exert a more pronounced ethanol-drug effect interaction than a higher ethanol concentration.