By Fearn T., Brown P.J., Besbeas P.
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Extra info for A Bayesian decision theory approach to variable selection for discrimination
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  that only one of the two bifurcating branches can be stable. Specifically, the positive equilibrium branch is stable near n = 1 if
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).