Saddle pattern resonance and onset of crisis to spatiotemporal chaos

Abstract

We observe a novel phenomenon which we call "pattern resonance." It occurs in a theoretical model when the realized wave solution evolves to about the same shape of a saddle steady-wave solution. Here the unstable saddle solution behaves like a "potential." We find that the resonance triggers the onset of a crisis, leading to a transition from temporal to spatiotemporal chaos. We also show that in our case the pattern resonance is essentially a nonlinear frequency resonance.