Fluctuation-driven Turing patterns

Abstract

Models of diffusion driven pattern formation that rely on the Turing mechanism are utilized in many areas of science. However, many such models suffer from the defect of requiring fine tuning of parameters or an unrealistic separation of scales in the diffusivities of the constituents of the system in order to predict the formation of spatial patterns. In the context of a very generic model of ecological pattern formation, we show that the inclusion of intrinsic noise in Turing models leads to the formation of "quasi-patterns" that form in generic regions of parameter space and are experimentally distinguishable from standard Turing patterns. The existence of quasi-patterns removes the need for unphysical fine tuning or separation of scales in the application of Turing models to real systems.

Minor changes to manuscript

References in corpus (4)

• Quasi-cycles in a spatial predator-prey model
• Amplified biochemical oscillations in cellular systems
• Fluctuations and Correlations in Lattice Models for Predator-Prey Interaction
• Predator-Prey Quasi-cycles from a Path Integral Formalism

Cited by in corpus (54)

• Stochastic population dynamics in spatially extended predator-prey systems
• Intrinsic noise in systems with switching environments
• Coevolution Maintains Diversity in the Stochastic "Kill the Winner" Model
• Giant amplification of noise in fluctuation-induced pattern formation
• Characterization of spiraling patterns in spatial rock-paper-scissors games
• Stochastic processes with distributed delays: chemical Langevin equation and linear-noise approximation
• Spatial interactions and oscillatory tragedies of the commons
• Turing instabilities in a mathematical model for signaling networks
• Key features of Turing systems are determined purely by network topology
• When does cyclic dominance lead to stable spiral waves?
• Population oscillations in spatial stochastic Lotka-Volterra models: A field-theoretic perturbational analysis
• Turing's diffusive threshold in random reaction-diffusion systems
• Stochastic waves in a Brusselator model with nonlocal interaction
• Patchiness and Demographic Noise in Three Ecological Examples
• Fluctuations and correlations in chemical reaction kinetics and population dynamics
• Imperfect Diffusion-Controlled Reactions
• Turing patterns on discrete topologies: from networks to higher-order structures
• Theoretical Analysis of Discreteness-Induced Transition in Autocatalytic Reaction Dynamics
• Feedbacks, Receptor Clustering, and Receptor Restriction to Single Cells yield large Turing Spaces for Ligand-receptor based Turing Models
• Path integral calculation for emergence of rapid evolution from demographic stochasticity
• Demographic noise and resilience in a semi-arid ecosystem model
• Precision and dissipation of a stochastic Turing pattern
• Turing instability in quantum activator-inhibitor systems
• Pinning of Diffusional Patterns by Non-Uniform Curvature
• A stochastic analysis of the spatially extended May-Leonard model
• Demographic noise and piecewise deterministic Markov processes
• Positive feedback can lead to dynamic nanometer-scale clustering on cell membranes
• Spatial patterns of competing random walkers
• Surface-tension-driven coarsening in mass-conserved reaction-diffusion systems
• Small-scale properties of a stochastic cubic-autocatalytic reaction-diffusion model
• Stabilizing spiral structures in the asymmetric May-Leonard model
• Fluctuations and the role of collision duration in reaction-diffusion systems
• Stochastic Description of a Bistable Frustrated Unit
• Stochastic lattice model of synaptic membrane protein domains
• Field theories and quantum methods for stochastic reaction-diffusion systems
• Noise-Induced Spatial Pattern Formation in Stochastic Reaction-Diffusion Systems
• Motif Analysis for Small-Number Effects in Chemical Reaction Dynamics
• Stochastic fluctuations and quasi-pattern formation in reaction-diffusion systems with anomalous transport
• Effect of demographic noise in a phytoplankton-zooplankton model of bloom dynamics
• Stochastic single-molecule dynamics of synaptic membrane protein domains
• Analyzing Diffusion and Flow-driven Instability using Semidefinite Programming
• Noise Sharing and Mexican Hat Coupling in a Stochastic Neural Field
• Distribution of randomly diffusing particles in inhomogeneous media
• Perturbative Field-Theoretical Analysis of Three-Species Cyclic Predator-Prey Models
• Pattern formation in individual-based systems with time-varying parameters
• Computation of random time-shift distributions for stochastic population models
• Plastic systemic inhibition controls amplitude while allowing phase pattern in a stochastic neural field model
• Computing macroscopic reaction rates in reaction-diffusion systems using Monte Carlo simulations
• Stochastic pattern formation and spontaneous polarisation: the linear noise approximation and beyond
• Stochastic Turing pattern formation in a model with active and passive transport
• Stochastic patterns in a 1D Rock-Paper-Scissor model with mutation
• Fluctuations in meta-population exclusion processes
• Rapidly forming, slowly evolving, spatial patterns from quasi-cycle Mexican Hat coupling
• Noise driven phase transitions in eco-evolutionary systems