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Similarly we can compare time scales of two variables

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Unformatted text preview: n the system has to be defined only at some discrete times only. In that case the question is ‘what should be time of discretization’? If time of discretization is small model may become detailed or if it is very large then we may get only average outputs only as fluctuations with time be lost – this will lead to a coarse model. Time scales: It indicates the duration of significant variations in a variable. For example if we consider populations of tiger and rabbits, then the population of tigers change very slowly as compared to that in rabbit population. If the duration of study is T and the time scale of a variable is T* such that T* >> T then this implies that there is hardly any change in the variable during the duration of the study and hence that parameter can be taken as ‘static’ – thus reducing the number of dynamic variables. Similarly we can compare time scales of two variables. This will be a process of simplification. If x(t) and y(t) are two dynamical variables such that changes in x cause changes in cause changes in y over time then only past values of x can influence the present and future of y not the reverse, i.e., y(t) is influenced by x() for < t and not for > t. This is called the principle of causality. Deterministic and Stochastic characterization: Depending on the uncertainty in the system we characterize it as deterministic/ stochastic. As such the real world is always unpredictable – however depending on the degree of uncertainty, we can make characterizations. If degree of uncertainty is small (as in the case of weight lifting problem! Or Rocket Launch Problem) we say the system is Deterministic otherwise it is Stochastic. We shall see some examples in the next lecture. Some System Characterizations ( L‐ 5) Now we shall consider some case studies and give a systems characterization for them. 1. Weight Lifting Problem: Here the goal of the study is to find a handicapping rule for a weight lifting competition, where no individual categories and the body weights of the lifters vary significantly. As we have seen earlier, the we...
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