A feature common to many models of vegetation pattern formation in semi-arid ecosystems is a sequence qualitatively different patterned states, "gaps -> labyrinth spots", that occurs as parameter representing precipitation decreases. We explore the robustness this "standard" generic setting bifurcation problem on hexagonal lattice, well particular reaction-diffusion model for formation. Specifically, we consider degeneracy equations creates small bubble space which stable small-amplitude...

We present a theoretical study of synchronization in N-element solid-state laser arrays. carry out the linear stability analysis for three types solution: nonlasing state, in-phase periodic and splayphase state. Both nearest-neighbor (on ring) coupling global (all-to-all) are treated; system symmetries enable us to solve problem arbitrary N. consider general case which coefficient iκ is complex find that depends crucially on sign imaginary part κ. In coupling, we discover surprising result:...

Competition between co-existing heteroclinic cycles that have a common connection is considered. A simple model problem, consisting of system ordinary differential equations in R4 with Z24 symmetry, analysed. The possess four hyperbolic fixed-points xi 1, 2, 3, and 4, connections joining pairs fixed points to form 'heteroclinic network'. network contains two 1 2 3 4 each which structurally stable respect perturbations preserve the symmetry problem. Local analysis, valid vicinity cycles,...

Equivariant bifurcation theory has been used extensively to study pattern formation via symmetry-breaking steady-state in various physical systems modelled by E(2)-equivariant partial differential equations. Much attention focused on solutions that are doubly periodic with respect a square or hexagonal lattice, for which the problem can be restricted finite-dimensional centre manifold. Previous studies have four- and six-dimensional representations lattice symmetry groups respectively, turn...

A complete classification of the generic D4*T2-equivariant Hopf bifurcation problems is presented. This arises naturally in study extended systems, invariant under Euclidean group E(2), when a spatially uniform quiescent state loses stability to waves wavenumber k not=0 and frequency omega not=0. The D4*T2 symmetry applies periodic boundary conditions are imposed two orthogonal horizontal directions. centre manifold theorem allows reduction infinite dimensional problem on C4. In normal form,...

Time-delays are common in many physical and biological systems they give rise to complex dynamic phenomena. The elementary processes involved template biopolymerization, such as mRNA protein synthesis, introduce significant time delays. However, there is not currently a systematic mapping between the individual mechanistic parameters delays these networks. We present here development of mathematical, time-delay models for translation, based on PDE models, which turn derived through...

A particular sequence of patterns, ‘gaps→labyrinth→spots’, occurs with decreasing precipitation in previously reported numerical simulations partial differential equation dryland vegetation models. These observations have led to the suggestion that this patterns can serve as an early indicator desertification some ecosystems. Because parameter values models take on a range plausible values, it is important investigate whether pattern prediction robust variation. For model, we find quantity...

Banded patterns consisting of alternating bare soil and dense vegetation have been observed in water-limited ecosystems across the globe, often appearing along gently sloped terrain with stripes aligned transverse to elevation gradient. In many cases, these bands are arced, field observations suggesting a link between orientation arcing relative grade curvature underlying terrain. We modify water transport Klausmeier model water–biomass interactions, originally posed on uniform hillslope,...

Recent experiments by Kudrolli, Pier, and Gollub [Physica D (to be published)] on surface waves, parametrically excited two-frequency forcing, show a transition from small hexagonal standing wave pattern to triangular ``superlattice`` pattern. We that generically the hexagons superlattice patterns bifurcate simultaneously flat state as forcing amplitude is increased, experimentally observed can described considering low-dimensional bifurcation problem. A number of predictions come out this...

view Abstract Citations (81) References (17) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS CO 7 -- 6 submillimeter emission from the glactic center : warm molecular gas and rotation curve in central 10 parsecs. Harris, A. I. ; Jaffe, D. T. Silber, M. Genzel, R. Bright J = 7-6 line pc of Galaxy has been mapped. This is first detection Galactic center; it was made with a new heterodyne spectrometer mounted on 3.0-m NASA IRTF telescope at Mauna Kea, Hawaii....

Climate change, amplified in the far north, has led to rapid sea ice decline recent years. In summer, melt ponds form on surface of Arctic ice, significantly lowering reflectivity (albedo) and thereby accelerating melt. Pond geometry controls details this crucial feedback; however, a reliable model pond does not currently exist. Here we show that simple voids surrounding randomly sized placed overlapping circles reproduces essential features patterns. The only two parameters, characteristic...

Motivated by experimental observations of exotic free surface standing wave patterns in the two-frequency Faraday experiment, we investigate role normal form symmetries associated pattern-selection problem. With forcing frequency components ratio m/n, where m and n are coprime integers that not both odd, there is possibility harmonic waves subharmonic may lose stability simultaneously, each with a different number. We focus on this situation compare case have longer wavelength than shorter...

The Faraday wave experiment is a classic example of system driven by parametric forcing, and it produces wide range complex patterns, including superlattice patterns quasipatterns. Nonlinear three-wave interactions between weakly damped modes play key role in determining which are favoured. We use this idea to design single multi-frequency forcing functions that produce examples quasipatterns new model PDE with forcing. make quantitative comparisons the predicted solutions PDE. Unexpectedly,...

[1] There is significant interest in whether there could be a bifurcation, sometimes referred to as “tipping point,” associated with Arctic sea ice loss. A low-order model of has recently been proposed and used argue that bifurcation summer loss (the transition from perennial seasonal ice) unlikely. Here bifurcations are investigated variation this incorporates additional effects, including parameterizations changes clouds heat transport lost. It shown can separate perennially seasonally...

Three-wave interactions form the basis of our understanding many pattern-forming systems because they encapsulate most basic nonlinear interactions. In problems with two comparable length scales, it is possible for waves shorter wavelength to interact one wave longer, as well longer shorter. Consideration both types three-wave can generically explain presence complex patterns and spatiotemporal chaos. Two scales arise naturally in Faraday experiment, results enable some previously...

In many drylands around the globe, vegetation self-organizes into regular spatial patterns in response to aridity stress. We consider regularly-spaced bands, on gentle hill-slopes, that survive low rainfall conditions by harvesting additional stormwater from upslope low-infiltration bare zones. are interested robustness of this pattern formation survival mechanism changes variability. For this, we use a flow-kick modeling framework treats storms as instantaneous kicks soil water. The...

For many years it was believed that an unstable periodic orbit with odd number of real Floquet multipliers greater than unity cannot be stabilized by the time-delayed feedback control mechanism Pyragas. A recent paper Fiedler et al. Phys. Rev. Lett. 98, 114101 (2007) uses normal form a subcritical Hopf bifurcation to give counterexample this theorem. Using Lorenz equations as example, we demonstrate stabilization identified for can also apply orbits created bifurcations in higher-dimensional...

We show how pattern formation in Faraday waves may be manipulated by varying the harmonic content of periodic forcing function. Our approach relies on crucial influence resonant triad interactions coupling pairs critical standing wave modes with damped, spatiotemporally modes. Under assumption weak damping and forcing, we perform a symmetry-based analysis that reveals damped most relevant for selection, strength corresponding depends frequencies, amplitudes, phases. In many cases, further...

Symmetry-breaking Hopf bifurcation problems arise naturally in studies of pattern formation. These equivariant bifurcations may generically result multiple solution branches bifurcating simultaneously from a fully symmetric equilibrium state. The theorem classifies these terms their symmetries, which involve combination spatial transformations and temporal shifts. In this paper, we exploit spatio-temporal symmetries to design non-invasive feedback controls select stabilize targeted branch,...