A Bayesian decision theory approach to variable selection by Fearn T., Brown P.J., Besbeas P.

By Fearn T., Brown P.J., Besbeas P.

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42) that v'(p) < 0 for all p > 0 and limp_,+00 v(p) = 0. 5 we find that x = 0 loses stability as n increases through 1. 2) and there exists a unique positive equilibrium these positive equilibria are (locally asymptotically) stable for n w 1 and are unbounded as n —> +00. , limt_+00 \x(t)\ = 0 for all x(0) > 0). In the preceding example only the facts that the submodels for the fertilities and transition probabilities tend monotonically to 0 as p increases without bound were used. Thus, other nonlinearities (or a mix of nonlinearities).

It is shown in [112] that only one of the two bifurcating branches can be stable. Specifically, the positive equilibrium branch is stable near n = 1 if 1. See Fig. 11. For large values of n the situation is more complicated, however; see [112]. 4 A case study Can mathematical models be used to describe and predict the dynamics of a real biological population? Can model predicted dynamics be observed in population data? Can predicted bifurcations in dynamics be observed in a population when DISCRETE MODELS 47 physical or biological parameters are changed?

D against the parameter b. In (a). 5. 20. To eliminate transients, 1000 iterations were performed before 100 values of p were plotted. in B,\ x R^_ and is (locally asymptotically) stable near the bifurcation point. The inequalities above (which are valid for all solutions, including equilibrium solutions) show that the magnitude of equilibria are bounded above by a multiple of n, and from this it follows that the spectrum of the continuum cannot be bounded (for if it were, then the global continuum would be bounded).

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