Regular transport dynamics produce chaotic travel times

Villalobos, Jorge; Muñoz, Vı́ctor; Rogan, José; Zarama, Roberto; Johnson, Neil F.; Toledo, B. A.; Valdivia, J. A.

doi:10.1103/physreve.89.062922

Cited by 5 publications

(4 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This effect was first noticed in Ref. 11. Furthermore, the width of the nontrivial and CR change as we change C, for longer waiting times it gets thinner.…”

Section: Model and Dynamics Descriptionsupporting

confidence: 74%

“…The dynamics of city traffic has become an active area of research not only because of its social and economical relevance, 1 but also and because it displays many interesting features [2][3][4][5][6][7][8][9][10][11] such as complex dynamics and emergent phenomena. [12][13][14] This complex behavior has been studied using many different approaches, going from statistical and cellular automaton, to hydrodynamical and mean field models.…”

Section: Introductionmentioning

confidence: 99%

“…11, and the discussion on the results presented in Ref. 11, derive analytical relations and restrictions for the parameters of the system, and study in detail the possible dynamics of the system.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modeling a bus through a sequence of traffic lights

Villalobos

Muñoz

Rogan

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

Self Cite

View full text Add to dashboard Cite

We propose a model of a bus traveling through a sequence of traffic lights, which is required to stop between the traffic signals to pick up passengers. A two dimensional model, of velocity and traveled time at each traffic light, is constructed, which shows non-trivial and chaotic behaviors for realistic city traffic parameters. We restrict the parameter values where these non-trivial and chaotic behaviors occur, by following analytically and numerically the fixed points and period 2 orbits. We define conditions where chaos may arise by determining regions in parameter space where the maximum Lyapunov exponent is positive. Chaos seems to occur as long as the ratio of the braking and accelerating capacities are greater than about ∼3.

show abstract

“…This effect was first noticed in Ref. 11. Furthermore, the width of the nontrivial and CR change as we change C, for longer waiting times it gets thinner.…”

Section: Model and Dynamics Descriptionsupporting

confidence: 74%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modeling a bus through a sequence of traffic lights

Villalobos

Muñoz

Rogan

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…There has been a growing interest in studying the evolution of these networks [8,9,23], and more recently, researchers have become interested in studying the network as a dynamical system in which a given object can be transported across the network, such as the propagation of rumors, infections [24,25], information packets [26,27], cars [28][29][30][31], buses [32,33], water [34], trains [35], citations [10], sand [36,37], earthquakes [38], etc. In this context, it has become of interest to study the distribution of the distances between nodes (as the shortest path along the network).…”

Section: Introductionmentioning

confidence: 99%

Generalization of the Ehrenfest urn model to a complex network

et al. 2015

Self Cite

View full text Add to dashboard Cite

The Ehrenfest urn model is extended to a complex directed network, over which a conserved quantity is transported in a random fashion. The evolution of the conserved number of packets in each urn, or node of the network, is illustrated by means of a stochastic simulation. Using mean-field theory we were able to compute an approximation to the ensemble-average evolution of the number of packets in each node which, in the thermodynamic limit, agrees quite well with the results of the stochastic simulation. Using this analytic approximation we are able to find the asymptotic dynamical state of the system and the time scale to approach the equilibrium state, for different networks. The study is extended to large scale-free and small-world networks, in which the relevance of the connectivity distribution and the topology of the network for the distribution of time scales of the system is apparent. This analysis may contribute to the understanding of the transport properties in real networks subject to a perturbation, e.g., the asymptotic state and the time scale required to approach it.

show abstract

The Stochastic Transport Dynamics of a Conserved Quantity on a Complex Network

Medina

Clark

Kiwi

et al. 2018

Sci Rep

Self Cite

View full text Add to dashboard Cite

The stochastic dynamics of conserved quantities is an emergent phenomena observed in many complex systems, ranging from social and to biological networks. Using an extension of the Ehrenfest urn model on a complex network, over which a conserved quantity is transported in a random fashion, we study the dynamics of many elementary packets transported through the network by means of a master equation approach and compare with the mean field approximation and stochastic simulations. By use of the mean field theory, it is possible to compute an approximation to the ensemble average evolution of the number of packets in each node which, in the thermodynamic limit, agrees quite well with the results of the master equation. However, the master equation gives a more complete description of the stochastic system and provides a probabilistic view of the occupation number at each node. Of particular relevance is the standard deviation of the occupation number at each node, which is not uniform for a complex network. We analyze and compare different network topologies (small world, scale free, Erdos-Renyi, among others). Given the computational complexity of directly evaluating the asymptotic, or equilibrium, occupation number probability distribution, we propose a scaling relation with the number of packets in the network, that allows to construct the asymptotic probability distributions from the network with one packet. The approximation, which relies on the same matrix found in the mean field approach, becomes increasingly more accurate for a large number of packets.

show abstract

Regular transport dynamics produce chaotic travel times

Cited by 5 publications

References 28 publications

Modeling a bus through a sequence of traffic lights

Modeling a bus through a sequence of traffic lights

Generalization of the Ehrenfest urn model to a complex network

The Stochastic Transport Dynamics of a Conserved Quantity on a Complex Network

Contact Info

Product

Resources

About