Comparative Analysis of Packet and Trigger Waves Originating from a Finite Wavelength Instability

Abstract

The finite wavelength instability generates trigger and packet waves in an extended three-variable Brusselatortype model. The trigger waves account for experimentally observed stacking (shock) structures and acceleration of oncoming waves before collision observed in the Belousov-Zhabotinsky system. Packet waves exhibit specular reflection from surfaces. The mouth of a narrow tube connected to a broader region acts as a semitransparent mirror for packet waves leaving the tube, with a coefficient of transparency that depends on the tube radius.

Diffusive instabilities in heterogeneous systems

“…For the wave instability, a complex eigenvalue has positive real part Re͑⌳͒ for some range of k and exhibits a maximum of Re͑⌳͒ at some finite k 0 . The characteristic wavelength of Turing patterns or waves ͑traveling or standing͒, 0 is equal to 2/k 0 ͑note that the wave instability can also produce trigger waves, in which case the wavelength 0 , has a different form 5 ͒.…”

Subcritical wave instability in reaction-diffusion systems

“…These features can be seen in Fig. 15,22 The amplitude of a SAWP depends on the initial perturbation and should change with time as t Ϫ1/2 exp(pt), where pХRe(⌳) max . The shape of these three peaks in time reflects the shape of the packet in space, and the width of a peak at half height multiplied by v g is approximately equal to the spatial width of the wave packet at the corresponding time.…”

“…4,15 Our motivation is that the character of the SHI at wave number kϭ0 may carry over to the wave instability at nonzero wave number k 0 , where the real part of the most positive eigenvalue of the Jacobian matrix has a maximum ͑see Fig. We start with a two-variable reaction-diffusion model that possesses a subcritical Hopf instability ͑SHI͒.…”

Localized stationary and traveling reaction-diffusion patterns in a two-layerA+B→oscillator system

“…To this end, we use here the Brusselator model, on which both dynamical and stationary instabilities can be explored and analytical progresses can be made [10,11,20,24,31,48,49]. We provide a first insight into the possible dynamics and coexistence of different instability modes in an A + B → oscillator system.…”