Sentence examples for condition of a Hopf from inspiring English sources

Next, we will prove the transversality condition of a Hopf bifurcation.

The conditions for existence of a Hopf bifurcation in a fractional order system are different from integer order systems.

Moreover, some studies showed the conditions for existence of a Hopf bifurcation [42 44] and the appearance of a limit cycle [45].

Moreover, the conditions for the existence of a Hopf bifurcation [14] are then satisfied.

Further, we can verify that the conditions for the occurrence of a Hopf bifurcation are satisfied.

In addition, conditions for the occurrence of a Hopf bifurcation are also presented.

The conditions for the existence of a Hopf bifurcation at the positive equilibrium are also presented.

Moreover, given a derivative order, the conditions for the existence of a Hopf bifurcation of the positive equilibrium are obtained.

In this study, we use the conditions for the existence of a Hopf bifurcation which were introduced by Xiang Li and Ranchao Wu [87].

It can be verified that the conditions for the occurrence of a Hopf bifurcation are also satisfied for system (22).

We then establish the conditions for the existence of a Hopf bifurcation at the positive equilibrium point as the order of derivatives crosses a critical value.