Sentence examples for main resonant cases from inspiring English sources

In this paper a further investigation is reported of periodically perturbed secondary bifurcations of the same system, which has more complicated phenomena in non-resonant, subharmonic or principal parametric resonant, and main resonant cases.

By applying the proposed technique, in the main resonant case, the problem of co-dimension 5 bifurcation, which has no symmetry property, is investigated.

The bifurcations in the subharmonic resonant case are Z2-symmetry ones and they have codimension 3. On the other hand, the bifurcations in the main resonant case are shown to possess no symmetry properties and their codimension increases to 5.

Non-resonant and primary resonance cases with and without internal resonance are illustrated and discussed.

Comparing the method developed here with other methods of computing the normal forms, it is understood that we may, respectively, obtain the normal forms, the coefficients of the normal forms and the associated near identity non-linear transformations for three resonant cases by using a same main Maple symbolic program.

The plots are almost identical away from the main resonant peak where the frequency location of the peaks are comparable but there is in some cases a 20% discrepancy in the magnitude of the peak value and in its bandwidth.

Non-resonant and some resonant cases will be studied for four different values of the relative errors.

For model 5 finite element error estimation the main resonant frequency of the rod exceeded 48%.

We choose the cross-diffusion coefficient as bifurcation parameter and discuss three different types of Turing bifurcations, corresponding to simple, double non-resonant and double resonant cases.

Then, the mode-locking motions, main resonant intervals, and subharmonic modes can be found.

The theory presented here can be applied to other higher order inner resonant cases as well.