Sentence examples for method and bifurcation from inspiring English sources

The equations of motion are studied by using the pseudo-arclength continuation method and bifurcation analysis.

The nonlinear equations of motion are numerically studied by using arclength continuation method and bifurcation analysis.

Numerical results are obtained by using the pseudo-arclength continuation method and bifurcation analysis.

The nonlinear equations of motion are studied by using arclength continuation method and bifurcation analysis.

Using the method and bifurcation theory, we present the existence and multiplicity of positive solutions for the nonlocal problems with the changes of the parameter.

Numerical integration (4th order Runge-Kutta method) and bifurcation analysis were performed with Xppaut (available at www.math.pitt.edu/~bard/xpp/xpp.html).edu/~bard/xpp/xpp.html

The variational method and bifurcations theory are used to con- struct a branch of nodal solutions.

Numerical results obtained by using pseudo-arclength continuation methods and bifurcation analysis show the nonlinear response at different flow velocities for (i) a fixed excitation amplitude and variable excitation frequency, and (ii) fixed excitation frequency by varying the excitation amplitude.

Therefore, in this study, the time step size h is chosen as a bifurcation parameter to study the existence of Hopf bifurcation for model (2) by using the normal form method and the bifurcation theory.

The Hopf bifurcation of HH model is controlled by applying a simple and unified state-feedback method and the bifurcation point is moved to an unreachable physiological point at the same time, so in this way an absolute bifurcation control is achieved.

Second, Melnikov's method is applied and bifurcation behaviour near the unperturbed homoclinic, heteroclinic and resonant periodic orbits is analyzed.