Phase-front solutions and instabilities in forced oscillations. (English) Zbl 0964.37016
Fiedler, B. (ed.) et al., International conference on differential equations. Proceedings of the conference, Equadiff ’99, Berlin, Germany, August 1-7, 1999. Vol. 2. Singapore: World Scientific. 1268-1274 (2000).
Summary: We study extended oscillatory systems that respond to uniform periodic forcing at one quarter of the forcing frequency. We find a new type of front instability where a stationary front shifting the oscillation phase by \(\pi\) decomposes into a pair of traveling fronts each shifting the phase by \(\pi/2\). The instability designates a transition from standing two-phase patterns, involving alternating domains with a phase shift of \(\pi\), to traveling four-phase patterns. A generalization of the instability to higher resonances is conjectured.
For the entire collection see [Zbl 0949.00026].
For the entire collection see [Zbl 0949.00026].
MSC:
| 37C75 | Stability theory for smooth dynamical systems |
| 37G15 | Bifurcations of limit cycles and periodic orbits in dynamical systems |
