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OPTIMAL CONTROL OF STOCHASTIC NON-LINEAR MODELS
IFAC Proceedings Volumes, 1989The use of large macroeconometric models has become central to the policy work of many national and international agencies. The models are not only complex in terms of their size but also invariably non-linear. Using such a model in policy formulation inevitably leads towards specifying a set of objectives and trying to meet these objectives as closely
S. G. Hall, M. J. Stephenson
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Non-linear compartmental models
Advances in Applied Probability, 1984The linear compartmental model arises when ‘particles’ move independently between (or out of) a system of compartments in a stochastically similar way. With a given ‘initial’ particle count, the subsequent compartmental particle counts follow multinomial probability distributions (Faddy (1976)) for Markov or semi-Markov movement processes.
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Application of non‐linear elastic model
International Journal for Numerical and Analytical Methods in Geomechanics, 1992AbstractThe properties of a previously published isotropic non‐linear elastic model with an elastic potential are illustrated in detail. Its parameter determination is elaborated and a parameter list is composed on the basis of published experimental data. The formulation with the elastic potential is shown to enable the minimization of numerical drift
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1997
Further models of two interacting quantities are studied in this chapter. These models are distinguished from those of the previous chapter because they lead to coupled non-linear, rather than linear, differential equations. Such equations usually cannot be solved explicitly.
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Further models of two interacting quantities are studied in this chapter. These models are distinguished from those of the previous chapter because they lead to coupled non-linear, rather than linear, differential equations. Such equations usually cannot be solved explicitly.
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Non-linear time series models for non-linear random vibrations
Journal of Applied Probability, 1980Non-linear time series models for non-linear vibrations are presented. Some typical behaviour of non-linear vibrations generated from Duffing's equation or van der Pol's equation are explained through the models.
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Non-linear threshold autoregressive models for non-linear random vibrations
Journal of Applied Probability, 1981Time series models for non-linear random vibrations are discussed from the viewpoint of the specification of the dynamics of the damping and restoring force of vibrations, and a non-linear threshold autoregressive model is introduced. Typical non-linear phenomena of vibrations are demonstrated using the models.
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2010
The linear theory of morphological stability, as shown in Chapter 10, predicts neither the explicit form nor the evolution dynamics of an unstable solid–liquid interface. Instead, linear theory predicts only the system’s initial unstable behavior—viz., evolution through exponential growth or decay—of a single-mode interface perturbation in the form of ...
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The linear theory of morphological stability, as shown in Chapter 10, predicts neither the explicit form nor the evolution dynamics of an unstable solid–liquid interface. Instead, linear theory predicts only the system’s initial unstable behavior—viz., evolution through exponential growth or decay—of a single-mode interface perturbation in the form of ...
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