Browsing by Author "Mobilia, M."

Now showing 1 - 8 of 8
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    Coexistence in the two-dimensional May-Leonard model with random rates
    He, Q.; Mobilia, M.; Täuber, Uwe C. (Springer, 2011-07-01)
    We employ Monte Carlo simulations to numerically study the temporal evolution and transient oscillations of the population densities, the associated frequency power spectra, and the spatial correlation functions in the (quasi-)steady state in two-dimensional stochastic May–Leonard models of mobile individuals, allowing for particle exchanges with nearest-neighbors and hopping onto empty sites. We therefore consider a class of four-state three-species cyclic predator-prey models whose total particle number is not conserved. We demonstrate that quenched disorder in either the reaction or in the mobility rates hardly impacts the dynamical evolution, the emergence and structure of spiral patterns, or the mean extinction time in this system. We also show that direct particle pair exchange processes promote the formation of regular spiral structures. Moreover, upon increasing the rates of mobility, we observe a remarkable change in the extinction properties in the May–Leonard system (for small system sizes): (1) As the mobility rate exceeds a threshold that separates a species coexistence (quasi-)steady state from an absorbing state, the mean extinction time as function of system size N crosses over from a functional form ∼ ecN /N (where c is a constant) to a linear dependence; (2) the measured histogram of extinction times displays a corresponding crossover from an (approximately) exponential to a Gaussian distribution. The latter results are found to hold true also when the mobility rates are randomly distributed.
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    Exact dynamics of a reaction-diffusion model with spatially alternating rates
    Mobilia, M.; Schmittmann, Beate; Zia, Royce K. P. (American Physical Society, 2005-05)
    We present the exact solution for the full dynamics of a nonequilibrium spin chain and its dual reaction-diffusion model, for arbitrary initial conditions. The spin chain is driven out of equilibrium by coupling alternating spins to two thermal baths at different temperatures. In the reaction-diffusion model, this translates into spatially alternating rates for particle creation and annihilation, and even negative "temperatures" have a perfectly natural interpretation. Observables of interest include the magnetization, the particle density, and all correlation functions for both models. Two generic types of time dependence are found: if both temperatures are positive, the magnetization, density, and correlation functions decay exponentially to their steady-state values. In contrast, if one of the temperatures is negative, damped oscillations are observed in all quantities. They can be traced to a subtle competition of pair creation and annihilation on the two sublattices. We comment on the limitations of mean-field theory and propose an experimental realization of our model in certain conjugated polymers and linear chain compounds.
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    Fluctuations and correlations in lattice models for predator-prey interaction
    Mobilia, M.; Georgiev, I. T.; Täuber, Uwe C. (American Physical Society, 2006-04-01)
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    Influence of local carrying capacity restrictions on stochastic predator-prey models
    Washenberger, M. J.; Mobilia, M.; Täuber, Uwe C. (IOP, 2007-02-14)
    We study a stochastic lattice predator–prey system by means of Monte Carlo simulations that do not impose any restrictions on the number of particles per site, and discuss the similarities and differences of our results with those obtained for site-restricted model variants. In accord with the classic Lotka–Volterra mean-field description, both species always coexist in two dimensions. Yet competing activity fronts generate complex, correlated spatio-temporal structures. As a consequence, finite systems display transient erratic population oscillations with characteristic frequencies that are renormalized by fluctuations. For large reaction rates, when the processes are rendered more local, these oscillations are suppressed. In contrast with site-restricted predator–prey model, we observe species coexistence also in one dimension. In addition, we report results on the steady-state prey age distribution.
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    Phase transitions and spatio-temporal fluctuations in stochastic lattice Lotka-Volterra models
    Mobilia, M.; Georgiev, I. T.; Täuber, Uwe C. (Springer, 2007-07-01)
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    Spatial rock-paper-scissors models with inhomogeneous reaction rates
    He, Q.; Mobilia, M.; Täuber, Uwe C. (American Physical Society, 2010-11-04)
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    Spatial stochastic predator-prey models
    Mobilia, M.; Georgiev, I. T.; Täuber, Uwe C. (2006)
    We consider a broad class of stochastic lattice predator-prey models, whose main features are overviewed. In particular, this article aims at drawing a picture of the influence of spatial fluctuations, which are not accounted for by the deterministic rate equations, on the properties of the stochastic models. Here, we outline the robust scenario obeyed by most of the lattice predator-prey models with an interaction "a' la Lotka-Volterra". We also show how a drastically different behavior can emerge as the result of a subtle interplay between long-range interactions and a nearest-neighbor exchange process.
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    Stochastic population dynamics in spatially extended predator-prey systems
    Dobramysl, U.; Mobilia, M.; Pleimling, Michel J.; Täuber, Uwe C. (2017-12-26)
    Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey competition invalidates the deterministic Lotka-Volterra picture of neutral population cycles. Stochastic models yield long-lived erratic population oscillations stemming from a resonant amplification mechanism. In spatially extended predator-prey systems, one observes noise-stabilized activity and persistent correlations. Fluctuation-induced renormalizations of the oscillation parameters can be analyzed perturbatively. The critical dynamics and the non-equilibrium relaxation kinetics at the predator extinction threshold are characterized by the directed percolation universality class. Spatial or environmental variability results in more localized patches which enhances both species densities. Affixing variable rates to individual particles and allowing for trait inheritance subject to mutations induces fast evolutionary dynamics for the rate distributions. Stochastic spatial variants of cyclic competition with rock-paper-scissors interactions illustrate connections between population dynamics and evolutionary game theory, and demonstrate how space can help maintain diversity. In two dimensions, three-species cyclic competition models of the May-Leonard type are characterized by the emergence of spiral patterns whose properties are elucidated by a mapping onto a complex Ginzburg-Landau equation. Extensions to general food networks can be classified on the mean-field level, which provides both a fundamental understanding of ensuing cooperativity and emergence of alliances. Novel space-time patterns emerge as a result of the formation of competing alliances, such as coarsening domains that each incorporate rock-paper-scissors competition games.