Chaos in Piecewisely Integrable Train Model for Two Blocks

Szkutnik, J.; Kułakowski, K.

doi:10.1142/s0129183102002924

Cited by 4 publications

(7 citation statements)

References 5 publications

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“…Nonlinear character of the velocity dependence of the friction force is not essential for the kind of motion. This result is in accordance with our previous conclusions on the train model of two blocks [19]. From the computational point of view, such a conclusion is optimistic, because the time of calculations is much shorter for a map than for a set of differential equations.…”

Section: Discussionsupporting

confidence: 91%

History-dependent synchronization in the Burridge-Knopoff Model

2003

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A three-blocks Burridge-Knopoff model is investigated. The dimensionless velocity-dependent friction force F (v) ∝ (1 + av) −1 is linearized around a = 0. In this way, the model is transformed into a six-dimensional mapping x(t n ) → x(t n+1 ), where t n are time moments when a block starts to move or stops. Between these moments, the equations of motion are integrable. For a < 0.1, the motion is quasiperiodic or periodic, depending on the initial conditions. For the periodic solution, we observe a synchronization of the motion of the lateral blocks. For a > 0.1, the motion becomes chaotic. These results are true for the linearized mapping, linearized numerical and non-linearized numerical solutions.

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Section: Discussionsupporting

confidence: 91%

History-dependent synchronization in the Burridge-Knopoff Model

2003

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“…The verification of this method has been described in Ref. 9. Additionally, we have to check whether the friction force changes sign -this would be a harmful artifact.…”

Section: The Systemmentioning

confidence: 92%

Generalized Synchronization and Memory Effect in the Burridge–knopoff System of Three Blocks

Szkutnik¹,

Kułakowski²

2004

Int. J. Mod. Phys. C

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Recently, synchronization in the Burridge-Knopoff model has been found to depend on the initial conditions. Here we report the existence of three modes of oscillations of the system of three blocks. In one of the modes, two lateral blocks are synchronized. In the second mode, the central block moves with almost constant velocity, i.e., it does not stick. Two lateral blocks do stick and they move in opposite phases. In the third mode, the blocks oscillate with aperiodic amplitude. The lateral blocks move in opposite phases and their frequency is lower than the one for the central block. The mode selected by the system depends on the initial conditions. Numerical results indicate that there is no modes in the phase space.

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“…As a result of the dragging effect of the conveyor belt, the chain is stretched and a complex-stick slip dynamics emerges. Both the case of one block alone [14,15,16,17,18,19] and the case of a chain formed by several blocks [14,16,20,21,22,23,24,25] were considered in previous theoretical and experimental studies. Coexistence of chaotic dynamics and SOC was observed by many authors [14,25].…”

Section: Introductionmentioning

confidence: 99%

A spring–block analogy for the dynamics of stock indexes

Sándor

Néda

2015

Physica A: Statistical Mechanics and its Applications

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A spring-block chain placed on a running conveyor belt is considered for modeling stylized facts observed in the dynamics of stock indexes. Individual stocks are modeled by the blocks, while the stock-stock correlations are introduced via simple elastic forces acting in the springs. The dragging effect of the moving belt corresponds to the expected economic growth. The spring-block system produces collective behavior and avalanche like phenomena, similar to the ones observed in stock markets. An artificial index is defined for the spring-block chain, and its dynamics is compared with the one measured for the Dow Jones Industrial Average. For certain parameter regions the model reproduces qualitatively well the dynamics of the logarithmic index, the logarithmic returns, the distribution of the logarithmic returns, the avalanche-size distribution and the distribution of the investment horizons. A noticeable success of the model is that it is able to account for the gain-loss asymmetry observed in the inverse statistics. Our approach has mainly a pedagogical value, bridging between a complex socio-economic phenomena and a basic (mechanical) model in physics.

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Chaos in Piecewisely Integrable Train Model for Two Blocks

Cited by 4 publications

References 5 publications

History-dependent synchronization in the Burridge-Knopoff Model

History-dependent synchronization in the Burridge-Knopoff Model

Generalized Synchronization and Memory Effect in the Burridge–knopoff System of Three Blocks

A spring–block analogy for the dynamics of stock indexes

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