Nonlinear Dynamical Economics and Chaotic Motion

Lorenz, Hans-Walter

doi:10.1007/978-3-662-22233-1

Cited by 175 publications

(95 citation statements)

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“…Typically, at a limit point of the sequence of perioddoubling bifurcation points of the parameter m, the price expectations will begin to oscillate in an aperiodic fashion, a telling sign of what has been coined deterministic chaos. (For a formal definition of chaos we refer the reader to Devaney 1989, Lorenz 1989, and Sandefur 1990, all excellent introductions to this topic). In fact, periodic cycles of arbitrary order k (including aperiodic cycles) will become visible.…”

Section: Stability Instability and Chaosmentioning

confidence: 99%

Stability and Chaos in Input Pricing for a Service Facility with Adaptive Customer Response to Congestion

Rump

Stidham

1998

Management Science

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We consider the stability of the equilibrium arrival rate and equilibrium admission price at a service facility, using a generalization of an input-pricing model introduced by Dewan and Mendelson and further examined by Stidham. At the equilibrium, the marginal value of service equals the admission price, that is, the sum of the admission fee and the expected delay cost. Stability means (roughly) that the system returns to the equilibrium after a perturbation, assuming the customers base their join/balk decisions on previous prices. We extend the discrete-time, dynamic-system pricing model of Stidham to allow adaptive expectations in which customers predict the future price based on a convex combination of the current price and the previous prediction. We show that this can lead to chaotic behavior when the equilibrium is unstable. That is, the price and arrival rate can follow aperiodic orbits, which appear to be completely random. Our results suggest an alternative explanation for observed variations in the mean arrival rate to a queueing system, which are often modeled by means of a random exogenous (e.g., Markovian) environment process.Optimal Pricing, Service Facility, Optimal Design of Queues, Stable Equilibrium, Chaos

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Section: Stability Instability and Chaosmentioning

confidence: 99%

Stability and Chaos in Input Pricing for a Service Facility with Adaptive Customer Response to Congestion

Rump

Stidham

1998

Management Science

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“…where x i (t − 1) is the value of the company's fitness at the previous round and F (x i (t − 1)) is a nonlinear map, to be specified later on, representing a business core equilibrium fitness, such that x−F (x i (t − 1)) < 0 signals negative factors, influencing a negative deviation with respect to the core equilibrium fitness value F (x i (t − 1)), while x − F (x i (t − 1)) > 0 signals positive factors, influencing a positive deviation with respect to the core equilibrium fitness value. Such potentials have been widely used within the economic modelling of business cycles (Gonçalves, 2012;Chen, 2008;Lorenz, 1997;Püu, 1997), being introduced here for the adaptive quantum computation process. Thus, in the harmonic oscillator potential, it is assumed that x − F (x i (t − 1)) < 0 is dampened by actions on the part of the company towards the recovery to the core equilibrium fitness, while x − F (x i (t − 1)) > 0 may be dampened by business growth sustainability restrictions, mainly linked to demand and market growth limits, much similar to ecosystemic limits to biological growth of a biological population.…”

Section: The Modelmentioning

confidence: 99%

“…• The problem of the economic equilibrium and the business cycle dynamics (Chen, 2008;Lorenz, 1997;Püu, 1997;Day, 1994Day, , 2000; • The problem of a business' economic risk and its financial consequences (Fama and Miller, 1972;Mandelbrot et al, 1997;Mandelbrot, 1997;Mandelbrot and Hudson, 2004);…”

Section: Introductionmentioning

confidence: 99%

“…The model operationalizes main theoretical notions of financial economics and business cycle economic theory, combining coupled map lattices with an evolutionary repeated quantum game, thus, bridging different evolutionary modelling approaches in both economics and finance, in particular: the chaos and nonlinear dynamics models (Day, 1994(Day, , 2000Lorenz, 1997;Püu, 1997) and the quantum models, which include both quantum financial game theory (Gonçalves and Gonçalves, 2008;Piotrowski and Sladkowski, 2001, 2008 and quantum financial economics (Baaquie et al, 2000;Baaquie and Marakani, 2001;Baaquie, 2004;Baaquie and Pan, 2011;Gonçalves, 2012;Schaden, 2002aSchaden, ,b, 2003Segal and Segal, 1998), both branches of the growing field of quantum econophysics Soloviev, 2009, 2011).…”

Section: Introductionmentioning

confidence: 99%

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Financial Turbulence, Business Cycles and Intrinsic Time in an Artificial Economy

Gonçalves

2012

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The coevolving coupled dynamics of financial markets and real economies is addressed through an integrated model of an artificial economy in which a population of competing companies have their shares traded in a financial market dominated by value investors and arbitrageurs that evaluate the companies' performance and adapt to market conditions. The coevolution between economy and financial market is operationalized through a quantum game that has by classical limit a coupled map lattice model with economic and financial chaotic dynamics. The connection between the business cycle, financial intrinsic time and scaling patterns of financial turbulence is addressed.

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“…Especially in the field of economics and sociology, the "costs" related to chaos have been frequently discussed (Lorenz, 1989;Gabisch and Lorenz, 1989). Those costs must be considered by the economic agents.…”

Section: Introductionmentioning

confidence: 99%

Active stabilization of a chaotic urban system

Haag

Hagel

Sigg

1997

Discrete Dynamics in Nature and Society

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A new method to stabilize dynamical systems by forcing the system variables into the desired unstable stationary point is proposed. The key conception of the method is based on parametric perturbation. This means that the equations of motion are influenced by continuous variation of some selected parameters. Thus-without using any external forces-the motion of the system approaches the chosen unstable stationary point. The variation of the parameters will vanish after the successful stabilization. Therefore, the system and its parameters are changed during the control process only. The algorithm is applied to an urban system within a metropolitan area obeying a Lorenz-type dynamics as well as to the Hnon attractor as an example for a discrete scenario.

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Nonlinear Dynamical Economics and Chaotic Motion

Cited by 175 publications

References 0 publications

Stability and Chaos in Input Pricing for a Service Facility with Adaptive Customer Response to Congestion

Stability and Chaos in Input Pricing for a Service Facility with Adaptive Customer Response to Congestion

Financial Turbulence, Business Cycles and Intrinsic Time in an Artificial Economy

Active stabilization of a chaotic urban system

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