DETERMINISTIC chaos is characterized by long-term unpredictability arising from an
extreme sensitivity to initial conditions. Such behaviour may be undesirable, particularly for …

The properties of excitable media are exploited to find minimum-length paths in complex
labyrinths. Optimal pathways are experimentally determined by the collection of time-lapse …

In this work, we analyze the linear stability of singular homoclinic stationary solutions and
spatially periodic stationary solutions in the one-dimensional Gray-Scott model. This stability …

Research on spatially extended excitable systems with cross-diffusion components is
reviewed. Particular attention is given to the new phenomena of the quasi-soliton and half …

A new geometrical criterion for the transition to spatio-temporal chaos (STC) arising in the
Gray–Scott model is presented. This is based on the inter-relationship of global bifurcating …

Self-replicating patterns (SRP) have been observed in several chemical reaction models,
such as the Gray–Scott (GS) model, as well as in physical experiments. Watching these …

In this paper we introduce a conceptual model for vegetation patterns that generalizes the
Klausmeier model for semi-arid ecosystems on a sloped terrain (Klausmeier in Science 284 …

The membrane and actin cortex of a motile cell can autonomously differentiate into two
states, one typical of the front, the other of the tail. On the substrate-attached surface of …

We consider a system of partial differential equations describing two spatially distributed
populations in a “predator-prey” interaction with each other. The spatial evolution is …

The dynamics and stability of multispot patterns to the Gray–Scott (GS) reaction-diffusion
model in a two-dimensional domain is studied in the singularly perturbed limit of small …