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Premature seizure of traffic flow due to the introduction of evolutionary games
Matjaž Perc, 2007, original scientific article

Abstract: We study the impact of evolutionary games on the flow of traffic. Since traffic participants do not always conform to the imposed rules, the introduction of games, i.e. set of strategies defining the behavioural pattern of agents on the road, appears justified. With this motivation, and the fact that individuals can change their strategy in the course of time, the evolutionary prisoner's dilemma game is introduced between neighbouring agents, enabling them to choose between cooperation and defection. Mutual cooperation enables forwarding to both agents for one step, while the defector is able to advance two steps when facing a cooperator, whereby the latter is forced to go one step backwards. Two defectors end up in a halt until the next iteration. Irrespective of their strategy, however, agents can move only if the road ahead is free. Jumps are never allowed. We show that this simple and plausible supplementation of the discrete cellular automaton Biham-Middleton-Levine (BML) model induces a traffic flow seizure by a substantially lower initial density of cars as in the absence of evolutionary games. The phenomenon is explained by studying the one-dimensional variant of the BML model with different advancement steps on the circular ring. In view of the proposed explanation, findings are generalized also to other types of games, such is the snowdrift game, and some statistical properties of gridlock formation in the presence of evolutionary rules are outlined. Our findings suggest that 'bending the law' results in a premature occurrence of traffic jams and thus unnecessarily burdens the transportation system.
Keywords: dynamic systems, traffic flow, theory of games, evolutionary rules, flow simulations, prisoner's dilemma
Published: 03.07.2017; Views: 465; Downloads: 319
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Nonlinear time series analysis of the human electrocardiogram
Matjaž Perc, 2005, professional article

Abstract: We analyse the human electrocardiogram with simple nonlinear time series analysis methods that are appropriate for graduate as well as undergraduate courses. In particular, attention is devoted to the notions of determinism and stationarity in physiological data. We emphasize that methods of nonlinear time series analysis can be successfully applied only if the studied data set originates from a deterministic stationary system. After positively establishing the presence of determinism and stationarity in the studied electrocardiogram, we calculate the maximal Lyapunov exponent, thus providing interesting insights into the dynamics of the human heart. Moreover, to facilitate interest and enable the integration of nonlinear time series analysis methods into the curriculum at an early stage of the educational process, we also provide user-friendly programs for each implemented method.
Keywords: dynamic systems, chaotic systems, nonlinear dynamics, electrocardiogram, human electrocardiogram, nonlinear analyses
Published: 07.06.2012; Views: 1838; Downloads: 73
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6.
Visualizing the attraction of strange attractors
Matjaž Perc, 2005, professional article

Abstract: We describe a simple new method that provides instructive insights into the dynamics of chaotic time-continuous systems that yield strange attractors as solutions in the phase space. In particular, we show that the norm of the vector field component that is orthogonal to the trajectory is an excellent quantity for visualizing the attraction of strange attractors, thus promoting the understanding of their formation and overall structure. Furthermore, based on the existence of zero orthogonal field strengths in planes that form low-dimensional strange attractors, we also provide an innovative explanation for the origin of chaotic behaviour. For instructive purposes, we first apply the method to a simple limit cycle attractor, and then analyse two paradigmatic mathematical models for classical time-continuous chaos. To facilitate the use of our method in graduate as well as undergraduate courses, we also provide user-friendly programs in which the presented theory is implemented.
Keywords: dynamic systems, chaotic systems, nonlinear dynamics, attractors, strange attractors
Published: 07.06.2012; Views: 1697; Downloads: 56
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7.
Spatial decoherence induced by small-world connectivity in excitable media
Matjaž Perc, 2005, original scientific article

Abstract: We study effects of different network topologies on the noise-induced pattern formation in a two-dimensional model of excitable media with FitzHugh-Nagumo local dynamics. In particular, we show that the introduction of long-range couplings induces decoherence of otherwise coherent noise-induced spatial patterns that can be observed by regular connectivity of spatial units. Importantly, already a small fraction of long-range couplings is sufficient to destroy coherent pattern formation. We argue that the small-world network topology destroys spatial order due to the lack of a precise internal spatial scale, which by regular connectivity is given by the coupling constant and the noise robust excursion time that is characteristic for the local dynamics. Additionally, the importance of spatially versus temporally ordered neural network functioning is discussed.
Keywords: dynamic systems, noise, spatiotemporal noise, intensity, spatial resonance, inherent spatial resonance, spatial decoherence, excitable media
Published: 07.06.2012; Views: 980; Downloads: 286
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8.
Double resonance in cooperation induced by noise and network variation for an evolutionary prisoner's dilemma
Matjaž Perc, 2006, original scientific article

Abstract: We study effects of slowly varying small-world topology and additive spatiotemporal random variations, introduced to the payoffs of a spatial prisoner's dilemma game, on the evolution of cooperation. We show that there exists an optimal fraction of shortcut links, constituting the variable complex network of participating players of the game, for which noise-induced cooperation is resonantly enhanced, thus marking a double resonance phenomenon in the studied system. The double resonance is attributed to the time-dependence of the connectivity structure that induces a tendency towards the mean-field behaviour in the limit of random graphs. We argue that random payoff disturbances and complex network topology are two potent extrinsic factors able to boost cooperation, thus representing a viable escape hatch out of evolutionary stalemate.
Keywords: dynamic systems, noise, spatiotemporal noise, intensity, spatial resonance, inherent spatial resonance, prisoner's dilemma
Published: 07.06.2012; Views: 1188; Downloads: 312
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9.
Evolutionary and dynamical coherence resonances in the pair approximated prisoner's dilemma game
Matjaž Perc, Marko Marhl, 2006, original scientific article

Abstract: Stochasticity has recently emerged as being a potent promoter of cooperative behaviour in systems developed under the framework of evolutionary game theory. In the spatial prisoner's dilemma game, the fitness of players adopting the cooperative strategy was found to be resonantly dependent on the intensity of payoff fluctuations. Evidently, the phenomenon resembles classical coherence resonance, whereby the noise-induced order, or coherence, of the dynamics is substituted with the noise-induced prevalence of the 'good' strategy, thus marking a constructive effect of noise on the system. The connection between the former 'dynamical' coherence resonance and the latter so-called 'evolutionary' coherence resonance, however, has not yet been established. The two different definitions of coherence resonance appear to provoke some discomfort. The goal of the present paper is therefore, on one hand, to draw a clear line between the two different perceptions of coherence resonance, and on the other, to show that the two apparently disjoint phenomena, that are currently related only by name, can in fact be observed simultaneously, sharing an identical mechanism of emergence.
Keywords: dynamic systems, noise, spatiotemporal noise, intensity, spatial resonance, inherent spatial resonance, spatial decoherence, excitable media
Published: 07.06.2012; Views: 1448; Downloads: 295
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10.
Thoughts out of noise
Matjaž Perc, 2006, original scientific article

Abstract: We study the effects of additive Gaussian noise on the behaviour of a simple spatially extended system, which is locally modelled by a nonlinear two-dimensional iterated map describing neuronal dynamics. In particular, we focus on the ability of noise to induce spatially ordered patterns, i. e. the so-called noise-induced pattern formation. For intermediate noise intensities, the spatially extended system exhibits ordered circular waves, thereby clearly manifesting the constructive role of random perturbations. The emergence of observed noise-induced patterns is explained with simple arguments that are obtained by analysing the typical spatial scale of patterns evoked by various diffusion coefficients. Since discrete-time systems are straightforward to implement and require modest computational capabilities, the present study describes one of the most fascinating and visually compelling examples of noise-induced self-organization in nonlinear systems in an accessible way for graduate or even advanced undergraduate students attending a nonlinear dynamics course.
Keywords: dynamic systems, chaotic systems, nonlinear dynamics, nonlinear systems, noise, nonlinear analyses
Published: 07.06.2012; Views: 1071; Downloads: 27
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