Breathing and wiggling motions in three-species laterally inhibitory systems

Holes and chaotic pulses of traveling waves coupled to a long-wave mode

“…Here we study numerically the regime outside the validity of that analysis and find pulses which propagate unsteadily, with periodically and aperiodically varying velocities. The phenomenon is quite similar to layer oscillations found in reaction-diffusion models [18,19].…”

“…The oscillations shown in figs. 2 and 5 are very similar to the breathing motion of localized structures found in reaction-diffusion systems [18,19]. They can be periodic [18] or chaotic [19].…”

Order parameter equations for front transitions: Planar and circular fronts

“…[42], which studies the effect of boundaries on spot dynamics, reports on the observation of stationary, breathing, and rebounding spots. Interaction between fronts may similarly lead to stationary, oscillating, and collapsing domains [10][11][12][13][14][15][16][17][18]. Recent experiments on the FerrocyanideIodate-Sulfite reaction show small oscillating chemical spots away from the reactor boundary that are most likely due to front interactions and/or curvature [43].…”

“…These motions can be driven by curvature [1,2], front interactions [3,4], convective instabilities [5,6], and external fields [7][8][9]. In some cases fronts reverse their direction of propagation, as for example in breathing pulses [10][11][12][13][14][15][16][17][18], where the reversal is periodic in time, and nucleation of spiral-vortex pairs, where the reversal is local along the extended front line [19][20][21][22][23].…”

Bound Pulse Trains in Arrays of Coupled Spatially Extended Dynamical Systems

“…This regime associated with the formation of locally coupled pulse trains bounded due to a balance of attraction and repulsion between them is different from the pulse bound states reported earlier in different laser, plasma, chemical, and biological systems. We propose a simplified analytical description of the observed phenomenon, which is in a good agreement with the results of direct numerical simulations of a model system describing an array of coupled mode-locked lasers.Nonlinear temporal pulses and spatial dissipative localized structures appear in various optical, plasma, hydrodynamic, chemical, and biological systems [1][2][3][4][5][6][7][8][9][10][11][12][13]. Being well-separated from each other these structures can interact locally via exponentially decaying tails and, as a result of this interaction, they can form bound states, known also as "dissipative soliton molecules" [14], characterized by fixed distances and phase differences between individual structures.…”