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Pulses and global bifurcations in a nonlocal reaction-diffusion system
Phys. Rev. E 48, 2917 – Published 1 October, 1993
DOI: https://doi.org/10.1103/PhysRevE.48.2917
Abstract
Experiments and simulations of simple reaction-diffusion systems in bounded domains with spatially nonlocal coupling display interesting pulse motions that are absent without the nonlocal effect. These include pulses that stick to the boundaries, ‘‘bounce’’ off them, or disappear at one boundary and reappear at the other, as if the domain was periodic. We numerically show that, for a two-variable model system, the transitions between these motions occur through global bifurcations. The transition from a wall-bound stationary front to a ‘‘back-and-forth’’ moving (bouncing) pulse occurs through a symmetric crisis. This motion evolves into a ‘‘unidirectional’’ motion, in which a pulse disappears at one boundary as a new one is born at the other, through a gluing bifurcation. The relationship between the spatiotemporal behavior and its phase-space representation is shown, as well as the importance of the nonlocal effect in creating the required global phase-space structure.
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