Fractional electronic circuit simulation of a nonlinear macroeconomic model

David, Sérgio Adriani; Fischer, C.; Machado, J. A. Tenreiro

doi:10.1016/j.aeue.2017.11.019

Cited by 20 publications

(7 citation statements)

References 27 publications

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“…In the framework of the deterministic chaos stage, many papers [89][90][91][92][93][94][95][96][97][98][99] have been devoted to the description of financial processes with memory. In some papers [100][101][102][103][104][105], economic models were considered.…”

Section: Deterministic Chaos Stage (Approach)mentioning

confidence: 99%

“…(6) Computer simulation for modeling the national economies in the framework of the fractional generalizations of the Gross domestic product (GDP) model was proposed by Inés Tejado, Duarte Valério, Nuno Valério, Pedro Pires [214][215][216][217][218][219][220] in 2014-2019, and by Dahui Luo, JinRong Wang, Michal Feckan in 2018 in the paper [221]. 7In addition, we may note the works with economic models that were proposed in [100][101][102][103][104][105] that are related to the deterministic chaos stage.…”

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confidence: 99%

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On History of Mathematical Economics: Application of Fractional Calculus

Tarasov

2019

Mathematics

182

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Modern economics was born in the Marginal revolution and the Keynesian revolution. These revolutions led to the emergence of fundamental concepts and methods in economic theory, which allow the use of differential and integral calculus to describe economic phenomena, effects, and processes. At the present moment the new revolution, which can be called “Memory revolution”, is actually taking place in modern economics. This revolution is intended to “cure amnesia” of modern economic theory, which is caused by the use of differential and integral operators of integer orders. In economics, the description of economic processes should take into account that the behavior of economic agents may depend on the history of previous changes in economy. The main mathematical tool designed to “cure amnesia” in economics is fractional calculus that is a theory of integrals, derivatives, sums, and differences of non-integer orders. This paper contains a brief review of the history of applications of fractional calculus in modern mathematical economics and economic theory. The first stage of the Memory Revolution in economics is associated with the works published in 1966 and 1980 by Clive W. J. Granger, who received the Nobel Memorial Prize in Economic Sciences in 2003. We divide the history of the application of fractional calculus in economics into the following five stages of development (approaches): ARFIMA; fractional Brownian motion; econophysics; deterministic chaos; mathematical economics. The modern stage (mathematical economics) of the Memory revolution is intended to include in the modern economic theory new economic concepts and notions that allow us to take into account the presence of memory in economic processes. The current stage actually absorbs the Granger approach based on ARFIMA models that used only the Granger–Joyeux–Hosking fractional differencing and integrating, which really are the well-known Grunwald–Letnikov fractional differences. The modern stage can also absorb other approaches by formulation of new economic notions, concepts, effects, phenomena, and principles. Some comments on possible future directions for development of the fractional mathematical economics are proposed.

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Section: Deterministic Chaos Stage (Approach)mentioning

confidence: 99%

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confidence: 99%

On History of Mathematical Economics: Application of Fractional Calculus

Tarasov

2019

Mathematics

182

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“…In recent years, people have tried to apply fractional order memristors to chaotic circuits and proposed some fractional order memristor-based chaotic systems [27][28][29], which also possess some complex dynamics, including chaos, hyperchaos, and coexisting attractors dependent on initial values. Many researches have also been done on fractional circuit simulation [30][31][32], and Reference [30] designed an electronic circuit to emulate the behavior of the fractional incommensurate order financial system. A fractional nonlinear macroeconomic dynamic model was simulated in Reference [31] using electronic circuit emulation by means of the Cadence OrCAD™ package.…”

Section: Introductionmentioning

confidence: 99%

“…Many researches have also been done on fractional circuit simulation [30][31][32], and Reference [30] designed an electronic circuit to emulate the behavior of the fractional incommensurate order financial system. A fractional nonlinear macroeconomic dynamic model was simulated in Reference [31] using electronic circuit emulation by means of the Cadence OrCAD™ package. In Reference [32], the fractional order memristor-based chaotic circuit was constructed by equivalent unit circuits.…”

Section: Introductionmentioning

confidence: 99%

A Nonvolatile Fractional Order Memristor Model and Its Complex Dynamics

Wang

et al. 2019

Entropy

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It is found that the fractional order memristor model can better simulate the characteristics of memristors and that chaotic circuits based on fractional order memristors also exhibit abundant dynamic behavior. This paper proposes an active fractional order memristor model and analyzes the electrical characteristics of the memristor via Power-Off Plot and Dynamic Road Map. We find that the fractional order memristor has continually stable states and is therefore nonvolatile. We also show that the memristor can be switched from one stable state to another under the excitation of appropriate voltage pulse. The volt–ampere hysteretic curves, frequency characteristics, and active characteristics of integral order and fractional order memristors are compared and analyzed. Based on the fractional order memristor and fractional order capacitor and inductor, we construct a chaotic circuit, of which the dynamic characteristics with respect to memristor’s parameters, fractional order α, and initial values are analyzed. The chaotic circuit has an infinite number of equilibrium points with multi-stability and exhibits coexisting bifurcations and coexisting attractors. Finally, the fractional order memristor-based chaotic circuit is verified by circuit simulations and DSP experiments.

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“…The fractional calculus (FC), as a branch of mathematical analysis, investigates the extension of deriva-tives and integrals to non-integer orders [1][2][3]. Nowadays, the new aspects of the FC are growing fast and its applications are found in different areas like chaos synchronization [4], diffusion equation [5], biology [6], control [7] and economic [8]. Additionally, the utility of the FC in the optimal control problems (OCPs) has attracted the attention of many researchers.…”

Section: Introductionmentioning

confidence: 99%

Untitled

2018

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The aim of this paper is to design an efficient numerical method to solve a class of time fractional optimal control problems. In this problem formulation, the fractional derivative operator is consid-ered in three cases with both singular and non-singular kernels. The necessary conditions are derived for the optimality of these problems and the proposed method is evaluated for different choices of derivative operators. Simulation results indicate that the suggested technique works well and pro-vides satisfactory results with considerably less computational time than the other existing methods. Comparative results also verify that the fractional operator with Mittag-Leffler kernel in the Caputo sense improves the performance of the controlled system in terms of the transient response compared to the other fractional and integer derivative operators.

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Fractional electronic circuit simulation of a nonlinear macroeconomic model

Cited by 20 publications

References 27 publications

On History of Mathematical Economics: Application of Fractional Calculus

On History of Mathematical Economics: Application of Fractional Calculus

A Nonvolatile Fractional Order Memristor Model and Its Complex Dynamics

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