Transitions between dissipative localized structures in the simplified Gilad-Meron model for dryland plant ecology

TL;DR

This paper investigates the organization and coexistence of localized vegetation patterns in a simplified dryland ecosystem model, revealing hybrid states and spatiotemporal dynamics in tristable regimes.

Contribution

It provides a bifurcation analysis of localized structures in a simplified Gilad-Meron model, highlighting the emergence of hybrid and oscillatory states in tristable ecosystems.

Findings

Localized spots and gaps coexist in tristable regimes.

Hybrid states emerge from the coexistence of different localized structures.

Spatiotemporal localized states appear in oscillatory regimes.

Abstract

Spatially extended patterns and multistability of possible different states is common in many ecosystems, and their combination has an important impact on their dynamical behaviours. One potential combination involves tristability between a patterned state and two different uniform states. Using a simplified version of the Gilad-Meron model for dryland ecosystems, we study the organization, in bifurcation terms, of the localized structures arising in tristable regimes. These states are generally related with the concept of wave front locking, and appear in the form of spots and gaps of vegetation. We find that the coexistence of localized spots and gaps, within tristable configurations, yield the appearance of hybrid states. We also study the emergence of spatiotemporal localized states consisting in a portion of a periodic pattern embedded in a uniform Hopf-like oscillatory background in a subcritical Turing-Hopf dynamical regime.