René G. Rojas

TL;DR: In this article, the effect of spatial discreteness over front propagation in an overdamped one-dimensional periodic lattice is studied, and the results of the discrete model, can be inferred by effective continuous equations with a supplementary spatially periodic term that they have denominated Peierls-Nabarro drift, which describes the bifurcation diagram of the front speed, the appearance of particle-type solutions and their snaking bifurlcation diagram.

TL;DR: This paper investigates the formation of stationary localized structures in the Brusselator model and establishes a bifurcation diagram showing the emergence of localized spots, and incorporates delayed feedback control.

TL;DR: In this paper, the authors present a unified description of localized states observed in systems with coexistence of two spatially periodic states, called bi-pattern systems, which are pinned over an underlying lattice that is either a self-organized pattern spontaneously generated by the system itself, or a periodic grid created by a spatial forcing.

TL;DR: In this paper, the formation of stationary localized structures in the Brusselator model is investigated by using numerical continuation methods in two spatial dimensions, and a bifurcation diagram showing the emergence of localized spots is established.

TL;DR: The dynamics of an interface connecting a stationary stripe pattern with a homogeneous state is studied and a nonresonate term is added to the Newell–Whitehead–Segel amplitude equation to describe this interface and its dynamics in a unified manner.