Chaos in a dynamic model of traffic flows in an origin-destination network

Zhang, Xiaoyan; Jarrett, David

doi:10.1063/1.166331

Cited by 23 publications

(11 citation statements)

References 3 publications

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“…In fact these authors give a very general result for dissipative maps of the plane into itself. However most specific examples discussed in the literature are neither conservative nor dissipative [27][28][29][30].…”

Section: Reverse Bifurcationsmentioning

confidence: 99%

Random Boolean network model exhibiting deterministic chaos

Matache

Heidel

2004

Phys. Rev. E

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This paper considers a simple Boolean network with N nodes, each node's state at time t being determined by a certain number of parent nodes, which may vary from one node to another. This is an extension of a model studied by Andrecut and Ali [Int. J. Mod. Phys. B 15, 17 (2001)]], who consider the same number of parents for all nodes. We make use of the same Boolean rule as Andrecut and Ali, provide a generalization of the formula for the probability of finding a node in state 1 at a time t, and use simulation methods to generate consecutive states of the network for both the real system and the model. The results match well. We study the dynamics of the model through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed point analysis. We show that the route to chaos is due to a cascade of period-doubling bifurcations which turn into reversed (period-halving) bifurcations for certain combinations of parameter values.

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Section: Reverse Bifurcationsmentioning

confidence: 99%

Random Boolean network model exhibiting deterministic chaos

Matache

Heidel

2004

Phys. Rev. E

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“…They proposed conditions for the existence, uniqueness, and stability of equilibrium in the deterministic model, and proposed conditions for stochastic process regularity in the stochastic model. Zhang and Jarrett [14] developed a dynamic model based on the conventional gravity model, which described the variations of OD flows over discrete-time periods. The authors showed that chaos occurs when the system dimension is relatively high.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Stability-To-Chaos in the Dynamic Evolution of Network Traffic Flows under a Dual Updating Mechanism

et al. 2018

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This paper proposes a traffic-flow evolutionary model under a dual updating mechanism that describes the day-to-day (DTD) dynamics of traffic flow and travel cost. To illustrate the concept, a simple two-route network is considered. Based on the nonlinear dynamic theory, the equilibrium stability condition of the system is derived and the condition for the division between the bifurcation and chaotic states of the system is determined. The characteristics of the DTD dynamic evolution of network traffic flow are investigated using numerical experiments. The results show that the system is absolutely stable when the sensitivity of travelers toward the route cost parameter (θ) is equal to or less than 0.923. The bifurcation appears in the system when θ is larger than 0.923. For values of θ equal to or larger than 4.402, the chaos appears in the evolution of the system. The results also show that with the appearance of chaos, the boundary and interior crises begin to appear in the system when θ is larger than 6.773 and 10.403, respectively. The evolution of network traffic flow is always stable when the proportion of travelers who do not change the route is 84% or greater.

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“…Chaotic behavior in a single vehicle-tra c light interaction [12] and two competing vehicles-tra c light interactions [13] was one (micro-level) aspect of the studies on tra c ow. Other studies relate to single facility (for example a freeway section), origindestination demand, and small-size networks [14,15].…”

Section: Introductionmentioning

confidence: 99%

Population Capacity Threats to Urban Area Resiliency: Observations on Chaotic Transportation Network Behavior

et al. 2016

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This paper is an endeavor to picture excessive population threats to the resiliency of a large metropolitan area. By employing an existing evolutionary model of tra c ow on a small expository network, we show how chaotic situations occur at certain demand and supply parameter values and try to address the questions: How may one determine city population capacity for its transportation network, what happens if the city passes this limit, or how may one return the city to a stable situation when it runs into unstable or chaotic situations. Under certain assumptions, the paper designs a simulation experiment to revisit the phenomenon discovered by Greenshields in 1934, but for a transportation network in a large city. A ow simulation shows that very small changes in the demand and supply of the network result in large variations in the throughput of the network, such that the time series of the latter values to an external observer are chaotic (with positive Lyapunov exponent). The limit to the resiliency of the city from the standpoint of its transportation network capacity is, then, estimated by a value for the city's population. It is then argued that how to take the network out of this situation.

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Chaos in a dynamic model of traffic flows in an origin-destination network

Cited by 23 publications

References 3 publications

Random Boolean network model exhibiting deterministic chaos

Random Boolean network model exhibiting deterministic chaos

Analysis of Stability-To-Chaos in the Dynamic Evolution of Network Traffic Flows under a Dual Updating Mechanism

Population Capacity Threats to Urban Area Resiliency: Observations on Chaotic Transportation Network Behavior

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