-
[show abstract]
[hide abstract]
ABSTRACT: The scarcity of water characterising drylands forces vegetation to adopt
appropriate survival strategies. Some of these generate water-vegetation
feedback mechanisms that can lead to spatial self-organisation of vegetation,
as it has been shown with models representing plants by a density of biomass,
varying continuously in time and space. However, although plants are usually
quite plastic they also display discrete qualities and stochastic behaviour.
These features may give rise to demographic noise, which in certain cases can
influence the qualitative dynamics of ecosystem models. In the present work we
explore the effects of demographic noise on the resilience of a model semi-arid
ecosystem. We introduce a spatial stochastic eco-hydrological hybrid model in
which plants are modelled as discrete entities subject to stochastic dynamical
rules, while the dynamics of surface and soil water are described by continuous
variables. The model has a deterministic approximation very similar to previous
continuous models of arid and semi-arid ecosystems. By means of numerical
simulations we show that demographic noise can have important effects on the
extinction and recovery dynamics of the system. In particular we find that the
stochastic model escapes extinction under a wide range of conditions for which
the corresponding deterministic approximation predicts absorption into desert
states.
arXiv:1209.2588. 09/2012;
-
[show abstract]
[hide abstract]
ABSTRACT: We explore a class of hybrid (piecewise deterministic) systems characterized
by a large number of individuals inhabiting an environment whose state is
described by a set of continuous variables. We use analytical and numerical
methods from nonequilibrium statistical mechanics to study the influence that
intrinsic noise has on the qualitative behavior of the system. We discuss the
application of these concepts to the case of semiarid ecosystems. Using a
system-size expansion we calculate the power spectrum of the fluctuations in
the system. This predicts the existence of noise-induced oscillations.
04/2012;
-
[show abstract]
[hide abstract]
ABSTRACT: We present an analysis of the price impact associated with single trades effected by different financial firms. Using data from the Spanish Stock Market, we find a high degree of heterogeneity across different market members, both in the instantaneous impact functions and in the time-dependent market response to trades by individual members. This heterogeneity is statistically incompatible with the existence of market-wide universal impact dynamics that apply uniformly to all trades and suggest that, rather, market dynamics emerge from the complex interaction of different behaviors of market participants. Several possible reasons for this are discussed, along with potential extensions one may consider to increase the range of applicability of existing models of market impact.
Physical Review E 03/2012; 85(3-2):036103. · 2.26 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: We extend recent analyses of stochastic effects in game dynamical learning to cases of multiplayer games and to games defined on networked structures. By means of an expansion in the noise strength we consider the weak-noise limit and present an analytical computation of spectral properties of fluctuations in multiplayer public goods games. This extends existing work on two-player games. In particular we show that coherent cycles may emerge driven by noise in the adaptation dynamics. These phenomena are not too dissimilar from cyclic strategy switching observed in experiments of behavioral game theory.
Physical Review E 10/2011; 84(4 Pt 1):041132. · 2.26 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: We present an analysis of the price impact associated with trades effected by
different financial firms. Using data from the Spanish Stock Market, we find a
high degree of heterogeneity across different market members, both in the
instantaneous impact functions and in the time-dependent market response to
trades by individual members. This heterogeneity is statistically incompatible
with the existence of market-wide universal impact dynamics which apply
uniformly to all trades and suggests that rather, market dynamics emerge from
the complex interaction of different behaviors of market participants. Several
possible reasons for this are discussed, along with potential extensions one
may consider to increase the range of applicability of existing models of
market impact.
09/2011;
-
[show abstract]
[hide abstract]
ABSTRACT: We show that intrinsic noise can induce spatiotemporal phenomena such as Turing patterns and traveling waves in a Brusselator model with nonlocal interaction terms. In order to predict and to characterize these stochastic waves we analyze the nonlocal model using a system-size expansion. The resulting theory is used to calculate the power spectra of the stochastic waves analytically and the outcome is tested successfully against simulations. We discuss the possibility that nonlocal models in other areas, such as epidemic spread or social dynamics, may contain similar stochastically induced patterns.
Physical Review E 08/2011; 84(2 Pt 2):026201. · 2.26 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: We extend recent analyses of stochastic effects in game dynamical learning to
cases of multi-player games, and to games defined on networked structures. By
means of an expansion in the noise strength we consider the weak-noise limit,
and present an analytical computation of spectral properties of fluctuations in
multi-player public good games. This extends existing work on two-player games.
In particular we show that coherent cycles may emerge driven by noise in the
adaptation dynamics. These phenomena are not too dissimilar from cyclic
strategy switching observed in experiments of behavioural game theory.
07/2011;
-
Tobias Galla
[show abstract]
[hide abstract]
ABSTRACT: Evolutionary game dynamics in finite populations is typically subject to noise, inducing effects which are not present in deterministic systems, including fixation and extinction. In the first part of this paper we investigate the phenomenon of drift reversal in finite populations, taking into account that drift is a local quantity in strategy space. Secondly, we study a simple imitation dynamics, and show that it can lead to fixation at internal mixed-strategy fixed points even in finite populations. Imitation in infinite populations is adequately described by conventional replicator dynamics, and these equations are known to have internal fixed points. Internal absorption in finite populations on the other hand is a novel dynamic phenomenon. Due to an outward drift in finite populations this type of dynamic arrest is not found in other commonly studied microscopic dynamics, not even in those with the same deterministic replicator limit as imitation.
Journal of Theoretical Biology 09/2010; 269(1):46-56. · 2.21 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: We use analytical techniques based on an expansion in the inverse system size to study the stochastic evolutionary dynamics of finite populations of players interacting in a repeated prisoner's dilemma game. We show that a mechanism of amplification of demographic noise can give rise to coherent oscillations in parameter regimes where deterministic descriptions converge to fixed points with complex eigenvalues. These quasicycles between cooperation and defection have previously been observed in computer simulations; here we provide a systematic and comprehensive analytical characterization of their properties. We are able to predict their power spectra as a function of the mutation rate and other model parameters and to compare the relative magnitude of the cycles induced by different types of underlying microscopic dynamics. We also extend our analysis to the iterated prisoner's dilemma game with a win-stay lose-shift strategy, appropriate in situations where players are subject to errors of the trembling-hand type.
Physical Review E 06/2010; 81(6 Pt 2):066122. · 2.26 Impact Factor
-
Tobias Galla
[show abstract]
[hide abstract]
ABSTRACT: Demographic noise has profound effects on evolutionary and population dynamics, as well as on chemical reaction systems and models of epidemiology. Such noise is intrinsic and due to the discreteness of the dynamics in finite populations. We here show that similar noise-sustained trajectories arise in game dynamical learning, where the stochasticity has a different origin: agents sample a finite number of moves of their opponents in between adaptation events. The limit of infinite batches results in deterministic modified replicator equations, whereas finite sampling leads to a stochastic dynamics. The characteristics of these fluctuations can be computed analytically using methods from statistical physics, and such noise can affect the attractors significantly, leading to noise-sustained cycling or removing periodic orbits of the standard replicator dynamics.
Physical Review Letters 11/2009; 103(19):198702. · 7.37 Impact Factor
-
Tobias Galla
[show abstract]
[hide abstract]
ABSTRACT: The effects of intrinsic noise on stochastic delay systems is studied within an expansion in the inverse system size. We show that the stochastic nature of the underlying dynamics may induce oscillatory behavior in parameter ranges where the deterministic system does not sustain cycles, and compute the power spectra of these stochastic oscillations analytically, in good agreement with simulations. The theory is developed in the context of a simple one-dimensional toy model, but is applicable more generally. Gene regulatory systems in particular often contain only a small number of molecules, leading to significant fluctuations in messenger RNA (mRNA) and protein concentrations. As an application we therefore study a minimalistic model of the expression levels of hes1 mRNA and Hes1 protein, representing the simple motif of an autoinhibitory feedback loop and motivated by its relevance to somite segmentation.
Physical Review E 08/2009; 80(2 Pt 1):021909. · 2.26 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: We study the effects of intrinsic noise on chemical reaction systems, which in the deterministic limit approach a limit cycle in an oscillatory manner. Previous studies of systems with an oscillatory approach to a fixed point have shown that the noise can transform the oscillatory decay into sustained coherent oscillations with a large amplitude. We show that a similar effect occurs when the stable attractors are limit cycles. We compute the correlation functions and spectral properties of the fluctuations in suitably comoving Frenet frames for several model systems including driven and coupled Brusselators, and the Willamowski-Rössler system. Analytical results are confirmed convincingly in numerical simulations. The effect is quite general, and occurs whenever the Floquet multipliers governing the stability of the limit cycle are complex, with the amplitude of the oscillations increasing as the instability boundary is approached.
Physical Review E 06/2009; 79(5 Pt 1):051131. · 2.26 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: Fluctuations and noise may alter the behavior of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in biological systems where a stable fixed point is found in the absence of noise. We here extend the theoretical analysis of such stochastic effects to models which have a limit cycle for some range of the model parameters. We formulate a description of fluctuations about the periodic orbit which allows the relation between the stochastic oscillations in the fixed point phase and the oscillations in the limit cycle phase to be elucidated. In the case of the limit cycle, a suitable transformation into a co-moving frame allow fluctuations transverse and longitudinal with respect to the limit cycle to be effectively decoupled. While longitudinal fluctuations are of a diffusive nature, those in the transverse direction follow a stochastic path more akin to an Ornstein-Uhlenbeck process. Their power spectrum is computed analytically within a van Kampen expansion in the inverse system size. This is carried out in two different ways, and the subsequent comparison with numerical simulations illustrates the effects that can occur due to diffusion in the longitudinal direction. Comment: 15 pages, 14 figures
05/2008;
-
[show abstract]
[hide abstract]
ABSTRACT: We study numerically and analytically the dynamics of defect formation during a finite-time quench of the two-dimensional Swift-Hohenberg (SH) model of Rayleigh-Bénard convection. We find that the Kibble-Zurek picture of defect formation can be applied to describe the density of defects produced during the quench. Our study reveals the relevance of two factors: the effect of local variations of the striped patterns within defect-free domains and the presence of both pointlike and extended defects. Taking into account these two aspects we are able to identify the characteristic length scale selected during the quench and to relate it to the density of defects. We discuss possible consequences of our study for the analysis of the coarsening process of the SH model.
Physical Review E 04/2003; 67(3 Pt 2):035101. · 2.26 Impact Factor
