Abstract. We derive sufficient conditions for stability and asymptotic stability of second order, scalar differential equations with differentiable coefficients.
Introduction.We study, for differentiable a 0 , a 1 : R ≥0 → R, stability properties of linear time-varying second-order differential equations of the form
In this paper we use the subdivision algorithm to approximate the box dimension of attractors of dynamical systems. Although in theory the subdivision algorithm provides a covering of the attractor with boxes of arbitrarily small diameter, in practice we have to overcome two obstructions: (1) ensure that the covering is (almost) minimal and (2) enhance the speed of convergence to the box dimension. We solve both problems and apply our results to the He´non, Lorenz, Ro¨ssler and Chua attractors. The method suggested in this paper uses information from several subdivision steps and converges to the box dimension much faster than the expression in the definition of the box dimension which uses only one covering of the attractor with boxes of a prescribed diameter.
We derive blending coefficients for the optimal blend of multiple independent prediction models with normal (Gaussian) distribution as well as the variance of the final blend. We also provide lower and upper bound estimation for the final variance and we compare these results with machine learning with counts, where only binary information (feature says yes or no only) is used for every feature and the majority of features agreeing together make the decision.
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