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A new model for vegetation patterns is introduced. The model reproduces a wide range of patterns observed in water-limited regions, including drifting bands, spots, and labyrinths. It predicts transitions from bare soil at low precipitation to homogeneous vegetation at high precipitation, through intermediate states of spot, stripe, and hole patterns. It(More)
A mathematical model for plant communities in water-limited systems is introduced and applied to a mixed woody-herbaceous community. Two feedbacks between biomass and water are found to be of crucial importance for understanding woody-herbaceous interactions: water uptake by plants' roots and increased water infiltration at vegetation patches. The former(More)
Ecosystem regime shifts are regarded as abrupt global transitions from one stable state to an alternative stable state, induced by slow environmental changes or by global disturbances. Spatially extended ecosystems, however, can also respond to local disturbances by the formation of small domains of the alternative state. Such a response can lead to gradual(More)
Domain walls in equilibrium phase transitions propagate in a preferred direction so as to minimize the free energy of the system. As a result, initial spatio-temporal patterns ultimately decay toward uniform states. The absence of a variational principle far from equilibrium allows the coexistence of domain walls propagating in any direction. As a(More)
Two major forms of vegetation patterns have been observed in drylands: nearly periodic patterns with characteristic length scales, and amorphous, scale-free patterns with wide patch-size distributions. The emergence of scale-free patterns has been attributed to global competition over a limiting resource, but the physical and ecological origin of this(More)
We investigate pattern formation in self-oscillating systems forced by an external periodic perturbation. Experimental observations and numerical studies of reaction-diffusion systems and an analysis of an amplitude equation are presented. The oscillations in each of these systems entrain to rational multiples of the perturbation frequency for certain(More)
The trade-off between the need to obtain new knowledge and the need to use that knowledge to improve performance is one of the most basic trade-offs in nature, and optimal performance usually requires some balance between exploratory and exploitative behaviors. Researchers in many disciplines have been searching for the optimal solution to this dilemma.(More)
Experiments on a quasi-two-dimensional Belousov–Zhabotinsky (BZ) reaction-diffusion system, periodically forced at approximately twice its natural frequency, exhibit resonant labyrinthine patterns that develop through two distinct mechanisms. In both cases, large amplitude labyrinthine patterns form that consist of interpenetrating fingers of(More)
Residential segregation in urban areas has been studied extensively by scientists from different fields, including economics, sociology, and population geography (see among The ongoing interest in this subject is the result, in part, of the common perception of residential segregation as an undesirable and even dangerous process. As commonly acknowledged,(More)
Two front instabilities in a reaction-diiusion system are shown to lead to the formation of complex patterns. The rst is an instability to transverse modulations that drives the formation of labyrinthine patterns. The second is a Nonequilibrium Ising-Bloch (NIB) bifurcation that renders a stationary planar front unstable and gives rise to a pair of(More)