Sentence examples for methods of dynamical from inspiring English sources

McMullen first used the methods of dynamical systems theory to show that generally convergent algorithms for solving polynomial equations exist only for polynomials of degree 3 or less.

We use methods of dynamical systems theory, such as fast-slow decomposition, averaging, and bifurcation analysis, to understand the multiple-timescale mechanisms underlying sigh generation in each model.

By applying methods of dynamical systems theory to a single-compartment model of a pre-BötC inspiratory neuron in [15], we explained in full detail how the MB solution results from these currents.

In this paper we use methods of dynamical systems theory to provide a precise mathematical characterization of the behavior of the point vortex Föppl system with a linear feedback control.

If the rate of change of the stimuli is rapid compared to that of the weights and threshold, then we can average over the fast time scale to get a mean field or averaged model and then study this through the usual methods of dynamical systems.

Using some qualitative reduction methods of dynamical system theory, the four-dimensional differential equation of motion is reduced to a two-dimensional one, and then the possible motions of the pipe are predicted through analyzing bifurcations of the solution to the reduced equation of motion.

For an actual dynamical system, the fractional generalized Hamiltonian method of constructing a fractional dynamical model is given, and then the six criterions for fractional generalized Hamiltonian method of dynamical stability are presented.

In the paper, we present fractional generalized Hamiltonian method of dynamical stability, in terms of Riesz Riemann Liouville derivative, and study its applications.

By using the method of dynamical systems and Congrove's results [21], Li and Zhang [1] investigated the exact explicit gap soliton, embedded soliton, periodic, and quasi-periodic wave solutions of the KdV-Sawada-Kotera-Ramani equation.

This paper describes a new method of dynamical state estimation for stochastic systems, in a practical case in which the observed data fluctuates within a finite amplitude domain owing to the dynamic range of the measurement instrument.

Jibin Li and Yishen Li [41] obtained the existence of solitary wave solutions, kink and antikink wave solutions, uncountable infinite many breaking wave solutions, and smooth and nonsmooth periodic wave solutions with the method of dynamical systems to the two-component generalization of the Camassa-Holm equation.