Fig. 9

Dispersion curve \(c=c(\varDelta)\) for a periodic travelling wave. Here c is the speed of a wave with period Δ. For small periods and on the upper branch waves are constructed that visit the domain where \(V< V_{-}\). Parameters as in Fig. 5. Solid lines represent periods where the system is stable while dashed lines represent where it is unstable; red dots represent the maximum stable period of the orbit, highlighting its increase with \(\tau_{h}\). Note that waves (on the lower branch of solutions) are stable for a large range of wave periods, and that the actual value of \((c,\varDelta)\) that would be observed in a simulation are dependent upon the choice of initial data