arXiv subjects

Tobias Galla

Publications and source records attributed to Tobias Galla.

At least 109 records · Page 6Linked to original sources

arXiv2011

Stochastic waves in a Brusselator model with nonlocal interaction

We show that intrinsic noise can induce spatio-temporal phenomena such as Turing patterns and travelling waves in a Brusselator model with nonlocal interaction terms. In order to predict and to characterize these quasi-waves we analyze the nonlocal model using a system-size expansion. The resulting theory is used to calculate the power spectra of the quasi-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.

cond-mat.stat-mech↗

arXiv2011

Complex dynamics in learning complicated games

Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditional game theory studies the equilibria of simple games. But is traditional game theory applicable if the game is complicated, and if not, what is? We investigate this question here, defining a complicated game as one with many possible moves, and therefore many possible payoffs conditional on those moves. We investigate two-person games in which the players learn based on experience. By generating games at random we show that under some circumstances the strategies of the two players converge to fixed points, but under others they follow limit cycles or chaotic attractors. The dimension of the chaotic attractors can be very high, implying that the dynamics of the strategies are effectively random. In the chaotic regime the payoffs fluctuate intermittently, showing bursts of rapid change punctuated by periods of quiescence, similar to what is observed in fluid turbulence and financial markets. Our results suggest that such intermittency is a highly generic phenomenon, and that there is a large parameter regime for which complicated strategic interactions generate inherently unpredictable behavior that is best described in the language of dynamical systems theory

nlin.CD↗

arXiv2011

Individual impact of agent actions in financial markets

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.

q-fin.TR↗

arXiv2011

Learning to play public good games

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.

physics.soc-ph↗

arXiv2011

Optimizing evacuation flow in a two-channel exclusion process

We use a basic setup of two coupled exclusion processes to model a stylised situation in evacuation dynamics, in which evacuees have to choose between two escape routes. The coupling between the two processes occurs through one common point at which particles are injected, the process can be controlled by directing incoming individuals into either of the two escape routes. Based on a mean-field approach we determine the phase behaviour of the model, and analytically compute optimal control strategies, maximising the total current through the system. Results are confirmed by numerical simulations. We also show that dynamic intervention, exploiting fluctuations about the mean-field stationary state, can lead to a further increase in total current.

physics.soc-ph↗

arXiv2011

Fixation and escape times in stochastic game learning

Evolutionary dynamics in finite populations is known to fixate eventually in the absence of mutation. We here show that a similar phenomenon can be found in stochastic game dynamical batch learning, and investigate fixation in learning processes in a simple 2x2 game, for two-player games with cyclic interaction, and in the context of the best-shot network game. The analogues of finite populations in evolution are here finite batches of observations between strategy updates. We study when and how such fixation can occur, and present results on the average time-to-fixation from numerical simulations. Simple cases are also amenable to analytical approaches and we provide estimates of the behaviour of so-called escape times as a function of the batch size. The differences and similarities with escape and fixation in evolutionary dynamics are discussed.

physics.soc-ph↗

arXiv2011

Cycles of cooperation and defection in imperfect learning

When people play a repeated game they usually try to anticipate their opponents' moves based on past observations, and then decide what action to take next. Behavioural economics studies the mechanisms by which strategic decisions are taken in these adaptive learning processes. We here investigate a model of learning the iterated prisoner's dilemma game. Players have the choice between three strategies, always defect (ALLD), always cooperate (ALLC) and tit-for-tat (TFT). The only strict Nash equilibrium in this situation is ALLD. When players learn to play this game convergence to the equilibrium is not guaranteed, for example we find cooperative behaviour if players discount observations in the distant past. When agents use small samples of observed moves to estimate their opponent's strategy the learning process is stochastic, and sustained oscillations between cooperation and defection can emerge. These cycles are similar to those found in stochastic evolutionary processes, but the origin of the noise sustaining the oscillations is different and lies in the imperfect sampling of the opponent's strategy. Based on a systematic expansion technique, we are able to predict the properties of these learning cycles, providing an analytical tool with which the outcome of more general stochastic adaptation processes can be characterised.

physics.soc-ph↗

arXiv2010

Imitation, internal absorption and the reversal of local drift in stochastic evolutionary games

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.

q-bio.PE↗

arXiv2010

Evolutionary dynamics, intrinsic noise and cycles of co-operation

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 quasi-cycles between co-operation 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.

q-bio.PE↗

arXiv2009

Intrinsic noise in game dynamical learning

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.

physics.soc-ph↗

arXiv2009

Independence and interdependence in the nest-site choice by honeybee swarms: agent-based models, analytical approaches and pattern formation

In a recent paper List, Elsholtz and Seeley [Phil. Trans. Roy. Soc. B. 364 (2009) 755] have devised an agent-based model of the the nest-choice dynamics in swarms of honeybees, and have concluded that both interdependence and independence are needed for the bees to reach a consensus on the best nest site. We here present a simplified version of the model which can be treated analytically with the tools of statistical physics and which largely has the same features as the original dynamics. Based on our analytical approaches it is possible to characterize the co-ordination outcome exactly on the deterministic level, and to a good approximation if stochastic effects are taken into account, reducing the need for computer simulations on the agent-based level. In the second part of the paper we present a spatial extension, and show that transient non-trivial patterns emerge, before consensus is reached. Approaches in terms of Langevin equations for continuous field variables are discussed.

q-bio.PE↗

arXiv2009

Minority games, evolving capitals and replicator dynamics

We discuss a simple version of the Minority Game (MG) in which agents hold only one strategy each, but in which their capitals evolve dynamically according to their success and in which the total trading volume varies in time accordingly. This feature is known to be crucial for MGs to reproduce stylised facts of real market data. The stationary states and phase diagram of the model can be computed, and we show that the ergodicity breaking phase transition common for MGs, and marked by a divergence of the integrated response is present also in this simplified model. An analogous majority game turns out to be relatively void of interesting features, and the total capital is found to diverge in time. Introducing a restraining force leads to a model akin to replicator dynamics of evolutionary game theory, and we demonstrate that here a different type of phase transition is observed. Finally we briefly discuss the relation of this model with one strategy per player to more sophisticated Minority Games with dynamical capitals and several trading strategies per agent.

physics.soc-ph↗

arXiv2009

Limit cycles, complex Floquet multipliers and intrinsic noise

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 co-moving Frenet frames for several model systems including driven and coupled Brusselators, and the Willamowski-Roessler 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.

cond-mat.stat-mech↗

arXiv2009

Stability and dynamical properties of material flow systems on random networks

The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are characteristic of flow networks in economic, ecological and biological systems. Based on results from random matrix theory, we work out the phase diagram of such systems defined on extensively connected random graphs, and study in detail how the choice of control policies and the network structure affects stability. We also present results for more complex topologies of the underlying graph, focussing on finitely connected Erdös-Réyni graphs, Small-World Networks and Barabási-Albert scale-free networks. Results indicate that variability of input-output matrix elements, and random structures of the underlying graph tend to make the system less stable, while fast price dynamics or strong responsiveness to stock accumulation promote stability.

cond-mat.dis-nn↗

arXiv2009

Intrinsic fluctuations in stochastic delay systems: theoretical description and application to a simple model of gene regulation

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 behaviour 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 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 auto-inhibitory feedback loop and motivated by its relevance to somite segmentation.

q-bio.MN↗

arXiv2008

Synchronization of coupled demographic oscillators

Demographic oscillators are individual-based systems exhibiting temporal cycles sustained by the stochastic dynamics of the microscopic interacting particles. We here use the example of coupled predator-prey oscillators to show that synchronization to a common frequency can occur between two such systems, even if they oscillate at different frequencies in the absence of coupling. The power spectra of the separate and the coupled systems are computed within a van Kampen expansion in the inverse system size, and it is found that they exhibit two peaks at separate frequencies at low coupling, but that only one peak is present at large enough coupling strength. We further make predictions on the time behaviour of the phases of the two oscillators, and their phase difference, and confirm the frequency entrainment at sufficiently large coupling. Theoretical results are verified convincingly in numerical simulations.

nlin.AO↗

arXiv2008

Spherical grand-canonical minority games with and without score discounting

We present a spherical version of the grand-canonical minority game (GCMG), and solve its dynamics in the stationary state. The model displays several types of transitions between multiple ergodic phases and one non-ergodic phase. We derive analytical solutions, including exact expressions for the volatility, throughout all ergodic phases, and compute the phase behaviour of the system. In contrast to conventional GCMGs, where the introduction of memory-loss precludes analytical approaches, the spherical model can be solved also when exponential discounting is taken into account. For the case of homogeneous incentives to trade epsilon and memory loss rates rho, an efficient phase is found only if rho=epsilon=0. Allowing for heterogeneous memory-loss rates we find that efficiency can be achieved as long as there is any finite fraction of agents which is not subject to memory loss.

physics.soc-ph↗

arXiv2008

Rank abundance relations in evolutionary dynamics of random replicators

We present a non-equilibrium statistical mechanics description of rank abundance relations (RAR) in random community models of ecology. Specifically, we study a multi-species replicator system with quenched random interaction matrices. We here consider symmetric interactions as well as asymmetric and anti-symmetric cases. RARs are obtained analytically via a generating functional analysis, describing fixed-point states of the system in terms of a small set of order parameters, and in dependence on the symmetry or otherwise of interactions and on the productivity of the community. Our work is an extension of Tokita [Phys. Rev. Lett. {\bf 93} 178102 (2004)], where the case of symmetric interactions was considered within an equilibrium setup. The species abundance distribution in our model come out as truncated normal distributions or transformations thereof and, in some case, are similar to left-skewed distributions observed in ecology. We also discuss the interaction structure of the resulting food-web of stable species at stationarity, cases of heterogeneous co-operation pressures as well as effects of finite system size and of higher-order interactions.

q-bio.PE↗