Double Hopf Bifurcation in Microbubble Oscillators with Delay Coupling

الملخص EN

Using center manifold reduction methodswe investigate the double Hopf bifurcation in the dynamics of microbubble with delay couplingwith main attention focused on nonresonant double Hopf bifurcation.

We obtain the normal form of the system in the vicinity of the double Hopf point and classify the bifurcations in a two-dimensional parameter space near the critical point.

Some numerical simulations support the applicability of the theoretical results.

In particularwe give the explanation for some physical phenomena of the system using the obtained mathematical results.