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Convective instability induced by two-points nonlocality

Zambrini, Roberta and Papoff, Francesco (2006) Convective instability induced by two-points nonlocality. Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 73 (1). 016611-016622. ISSN 1063-651X

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We consider diffusive nonlinear systems with nonlocal two-points coupling, generally induced by misalignment in optical feedback. We expand the stability analysis in F. Papoff and R. Zambrini [Phys. Rev. Lett. 94, 243903 (2005)] to determine convective and absolute thresholds. Nonlocality leads to different effects in comparison to well-known problems with drift, as the existence of opposite phase and group velocities for some modes and an instability region. The theoretical predictions are in agreement with numerical results in a nonlocal system with saturable nonlinearity over wide parameter regions. The knowledge of the stability diagram for any uniform state allows us to interpret the rich dynamics due to the interplay between finite size, noise, and multiple states.