Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1403.5959

Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in

Daniele Avitabile·Rebecca Hoyle·Giovanni Samaey
View original source ↗Read source document ↗Export metadata ↓

Abstract

We investigate coarse equilibrium states of a fine-scale, stochastic agent-based model of consumer lock-in in a duopolistic market. In the model, agents decide on their next purchase based on a combination of their personal preference and their neighbours' opinions. For agents with independent identically-distributed parameters and all-to-all coupling, we derive an analytic approximate coarse evolution-map for the expected average purchase. We then study the emergence of coarse fronts when spatial segregation is present in the relative perceived quality of products. We develop a novel Newton-Krylov method that is able to compute accurately and efficiently coarse fixed points when the underlying fine-scale dynamics is stochastic. The main novelty of the algorithm is in the elimination of the noise that is generated when estimating Jacobian-vector products using time-integration of perturbed initial conditions. We present numerical results that demonstrate the convergence properties of the numerical method, and use the method to show that macroscopic fronts in this model destabilise at a coarse symmetry-breaking bifurcation.

Explore related subjects

nlin.PS

Keep this discovery

BibTeXRIS

Daniele Avitabile, Rebecca Hoyle, Giovanni Samaey. 2014-03-24. Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in. https://doi.org/10.1137/140962188

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Self-similar vector solitons for the coupled higher-order nonlinear Schrodinger equations in inhomogeneous optical fibers

We prove the existence of two kinds of self-similar vector solitons in an inhomogeneous optical fiber medium, where light propagation is governed by a pair of coupled higher-order nonlinear Schrodinger equations with varying second- and third-order dispersions, self- and cross-phase modulation non linearities, self-steepening, and linear gain/loss effects. The newly found self-similar waves comprise bright-W-shaped and kink-antikink waveforms with nonvanishing amplitudes. As a practical exam ple, we discuss the propagation dynamics of these soliton structures in a periodically distributed fiber system as well as an exponential dispersion-decreasing fiber. The results demonstrate that the parameter functions of gain/loss and third-order dispersion serve as a key factor in determining the nonlinear dynamics of self-similar vector solitons. In particular, we find that precise control over the shape and dynamic evolution of self-similar pulses can be achieved through a proper choice of the distributed third-order dispersion parameter, while the gain/loss coefficient controls their intensity.

nlin.PS↗
arXiv2026

Fast Synergetic Simulation to Study Slow Evolution of Soliton Patterns in Optical Resonators

Complex patterns in physical and biological systems often emerge through slow collective dynamics governed by a small number of key variables. In nonlinear optical resonators, dissipative Kerr solitons provide an important example, where interactions between well-separated solitons can evolve over timescales far longer than the characteristic loss and gain timescales. Direct numerical simulation of these dynamics is challenging because stiffness forces conventional methods to resolve many rapidly damped degrees-of-freedom with very small time steps. We present a numerical scheme, the synergetic method, that eliminates these rapidly damped degrees-of-freedom and retains the slowly evolving modes, enabling time steps many orders of magnitude larger than those used in conventional approaches. Applied to soliton molecules in driven Kerr cavities, the method achieves speedups of $10^3$ to $10^5$ while capturing dynamics on laboratory timescales. We use it to model the full interaction dynamics of a three-soliton molecule and the evolution of an eight-soliton molecule. The approach provides an efficient framework for studying slow pattern formation in nonlinear systems with widely separated timescales.

nlin.PS↗
arXiv2026

Breathers in solitonic room-temperature superlattice-induced superfluorescence in quasi-2D perovskites

Recently, a soliton mechanism for room-temperature superfluorescence in thin perovskite films has been proposed, with a fundamental soliton predicted to remain stable under LO phonon--exciton interactions. At the same time, superlattice architectures offer a route to enhancing superfluorescence in perovskites. Motivated by recent observations of room-temperature superfluorescence in periodic superlattices of quasi-2D metal-halide perovskites, we extend the 2D nonlocal nonlinear Schr\"odinger equation describing Wannier exciton--LO phonon interactions to superlattice structures, obtaining a 3D nonlocal nonlinear Schr\"odinger equation. We show that interlayer tunnelling gives rise to breather dynamics corresponding to a stable fundamental soliton in mixed coordinate--momentum space, with the coordinate parallel to the layers and the momentum perpendicular to them. The breather dynamics originate from miniband formation, which induces a momentum-dependent phase modulation of the soliton. In the absence of interlayer tunnelling, the breather dynamics disappear and the soliton becomes stationary. These results establish a direct connection between interlayer tunnelling, miniband formation and soliton dynamics, suggesting that breather behavior can provide a signature of interlayer tunnelling in quasi-2D perovskite superlattices.

nlin.PS↗