Statistical Physics and Economics: Concepts, Tools and Applications

Schulz, Michael

doi:10.1007/0-387-21713-4

Cited by 25 publications

(21 citation statements)

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“…For simplicity, we assume the price splashes (bursts) are periodic with period T>0 and we will describe them by the Dirac delta-function, which is a generalized function [23,24]. The Dirac delta-function has an important role in modern economics and finance [25,26,27]. In general, it is possible to consider different values of the intervals between the bursts of the price.…”

Section: Equation Of Logistic Growth With Memory and Crisesmentioning

confidence: 99%

“…This map is used to describe different economic processes [32,33,34,35]. As a result, we can state that the standard logistic map (27) can be derived from the logistic differential equation (3)…”

Section: Economic Maps With Memory and Logistic Maps With Memorymentioning

confidence: 99%

“…It is known that the standard logistic map (27), which does not take into account the memory effects, can give the chaotic behavior [4, p. 33-67] and [5,6]. Using the logistic map (27), which is derived from economic model (15) with α=1, we can state that the sudden changes of price in the form of price splashes could lead to deterministic chaotic phenomena. The suggested logistic map with memory, its generalizations and the proposed economic discrete maps with memory can demonstrate a new chaotic behavior.…”

Section: )mentioning

confidence: 99%

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Logistic map with memory from economic model

Tarasova

Tarasov

2017

Chaos, Solitons & Fractals

111

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Abstract.A generalization of the economic model of logistic growth, which takes into account the effects of memory and crises, is suggested. Memory effect means that the economic factors and parameters at any given time depend not only on their values at that time, but also on their values at previous times. For the mathematical description of the memory effects, we use the theory of derivatives of non-integer order. Crises are considered as sharp splashes (bursts) of the price, which are mathematically described by the delta-functions. Using the equivalence of fractional differential equations and the Volterra integral equations, we obtain discrete maps with memory that are exact discrete analogs of fractional differential equations of economic processes. We derive logistic map with memory, its generalizations, and "economic" discrete maps with memory from the fractional differential equations, which describe the economic natural growth with competition, power-law memory and crises.Keywords: model of logistic growth, logistic map, chaos, discrete map with memory, hereditarity, memory effects, power-law memory, derivatives of non-integer order MSC: 26A33; 34A08

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Section: Equation Of Logistic Growth With Memory and Crisesmentioning

confidence: 99%

Section: Economic Maps With Memory and Logistic Maps With Memorymentioning

confidence: 99%

Section: )mentioning

confidence: 99%

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Logistic map with memory from economic model

Tarasova

Tarasov

2017

Chaos, Solitons & Fractals

111

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“…On the other hand, statistical physics is a wellestablished field with many interdisciplinary applications in recent decades, in particular with regards to criticality and phase transitions [13][14][15]. Accordingly, connections between quantum information theory and classical statistical mechanics has attracted much attention recently [16][17][18][19][20][21], which has led to cross-fertilization.…”

Section: Introductionmentioning

confidence: 99%

Dual correspondence between classical spin models and quantum Calderbank-Shor-Steane states

Zarei

Montakhab

2018

Phys. Rev. A

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The correspondence between classical spin models and quantum states has attracted much attention in recent years. However, it remains an open problem as to which specific spin model a given (well-known) quantum state maps to. Here, we provide such an explicit correspondence for an important class of quantum states where a duality relation is proved between classical spin models and quantum Calderbank-Shor-Steane (CSS) states. In particular, we employ graph-theoretic methods to prove that the partition function of a classical spin model on a hypergraph H is equal to the inner product of a product state with a quantum CSS state on a dual hypergraphH. We next use this dual correspondence to prove that the critical behavior of the classical system corresponds to a relative stability of the corresponding CSS state to bit-flip (or phase-flip) noise, thus called critical stability. We finally conjecture that such critical stability is related to the topological order in quantum CSS states, thus providing a possible practical characterization of such states.

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“…Complex networks have been shown to characterize the behavior and topological organization of many natural and engineered systems, such as those found in the disciplines of sociology [3], biology [4], finance [5], communication networks [6], sensor networks etc. A common feature across all these multi-agent systems is that their global behavior emerges from local dynamics of the participating agents.…”

Section: Introductionmentioning

confidence: 99%

Critical phenomena and finite-size scaling in communication networks?

Sarkar

Mukherjee

Srivastav

et al. 2010

Proceedings of the 2010 American Control Conference

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This paper presents a statistical mechanics-based approach to investigate critical phenomena and size scaling in communication networks. The qualitative nature of phase transitions in the underlying network systems is characterized; and its static and dynamic critical behaviors are identified. Effects of network size, different routing strategies have been analyzed. In all these analyses, phase transition is considered using a single intensive parameter of the communication network system, namely the external packet load. These problems have been investigated by extensive simulation on the model of a wired communication network.

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Statistical Physics and Economics: Concepts, Tools and Applications

Abstract: Statistical physics and economics : concepts, tools, and applications I Michael Schulz. p. ern. -(Springer tracts in modern physics ; 184) Includes bibliographical references and index.

Cited by 25 publications

References 0 publications

Logistic map with memory from economic model

Logistic map with memory from economic model

Dual correspondence between classical spin models and quantum Calderbank-Shor-Steane states

Critical phenomena and finite-size scaling in communication networks?

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