Chaos in economic models with exogenous shocks

Akhmet, Marat; Akhmetova, Zhanar; Fen, Mehmet Onur

doi:10.1016/j.jebo.2014.06.008

Cited by 30 publications

(27 citation statements)

References 37 publications

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“…In our previous papers [2,5,6,7,8] we analyzed the extension of chaos when the base system possesses an asymptotically stable equilibrium. The present paper focuses mostly on the generation of cyclic chaos through unilateral coupling of multiple systems.…”

Section: The Input-output Mechanism and Its Applicationsmentioning

confidence: 99%

“…Using the results of [2,5,6], one can state that the chaoticity of the logistic map A 1 with µ = 3.8 makes the function ν 1 (t, θ) behave chaotically, and system A 2 is chaotic through period-doubling cascade for the same value of the parameter µ. That is, it admits infinitely many unstable periodic solutions and exhibits sensitivity.…”

Section: Description Of the Models A 1 To Amentioning

confidence: 99%

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Exogenous Versus Endogenous for Chaotic Business Cycles

Akhmet

Akhmetova²,

Fen³

2016

DNC

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We propose a novel approach to generate chaotic business cycles in a deterministic setting. Rather than producing chaos endogenously, we consider aggregate economic models with limit cycles and equilibriums, subject them to chaotic exogenous shocks and obtain chaotic cyclical motions. Thus, we emphasize that chaotic cycles, which are inevitable in economics, are not only interior properties of economic models, but also can be considered as a result of interaction of several economical systems. This provides a comprehension of chaos (unpredictability, lack of forecasting) and control of chaos as a global economic phenomenon from the deterministic point of view.We suppose that the results of our paper are contribution to the mixed exogenous-endogenous theories of business cycles in classification by P.A. Samuelson [76]. Moreover, they demonstrate that the irregularity of the extended chaos can be structured, and this distinguishes them from the generalized synchronization. The advantage of the knowledge of the structure is that by applying instruments, which already have been developed for deterministic chaos one can control the chaos, emphasizing a parameter or a type of motion. For the globalization of cyclic chaos phenomenon we utilize new mechanisms such that entrainment by chaos, attraction of chaotic cycles by equilibriums and bifurcation of chaotic cycles developed in our earlier papers.

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Section: The Input-output Mechanism and Its Applicationsmentioning

confidence: 99%

Section: Description Of the Models A 1 To Amentioning

confidence: 99%

Exogenous Versus Endogenous for Chaotic Business Cycles

Akhmet

Akhmetova²,

Fen³

2016

DNC

Self Cite

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“…And the tangential bifurcation and intermittent chaos were reported by numerical simulations. In [4], the generation of chaos in economic models through exogenous shocks was investigated. And a rigorous proof of the existence of chaos in the perturbed model was given and the results shed light on a novel source of chaos in economic models.…”

Section: Introductionmentioning

confidence: 99%

Chaos Control and Anticontrol of the Output Duopoly Competing Evolution Model

Zhang

2017

Discrete Dynamics in Nature and Society

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In the process of social development, there are a lot of competitions and confrontations. Participants in these competitions and confrontations always have different interests and goals. In order to achieve their goals, the participants must consider the opponent's strategy to adjust their own strategies to achieve the interests of the optimization. This is called game. Based on the definition and its stability of the passive system, the passive control items are designed to the output of the duopoly competition evolution model, and the efficacy of the control methods is shown by the Lyapunov indexes. Then, the optimal function control method is taken to carry on the chaotic anticontrol to the chaotic system, and the Lyapunov indexes illustrate the control result. At last, the chaotic game of the system is introduced by combining the chaos control and anticontrol.

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“…Our suggestion may be a key to explain why the weather unpredictability is observed everywhere. This is true also for unpredictability and lack of forecasting in economics [21,22]. To complete the explanation of weather and economical unpredictability as global phenomena by the analysis of interconnected models, we need to argument persistence of chaos of a model against chaotic perturbations as solutions of another similar models.…”

Section: Introductionmentioning

confidence: 99%

“…For such a value of the parameter, the interval [0, 1] is invariant under the iterations of (1.5) [28]. An interpretation of the relay system (1.2) from the economic point of view can be found in [21]. According to the results of papers [19,29], one can confirm that system (1.2) is Li-Yorke chaotic under certain conditions, which will be given in the next section.…”

Section: Introductionmentioning

confidence: 99%

Persistence of Li–Yorke chaos in systems with relay

Akhmet¹,

Fen²,

Kashkynbayev³

2017

Electron. J. Qual. Theory Differ. Equ.

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It is rigorously proved that the chaotic dynamics of the non-smooth system with relay function is persistent even if a chaotic perturbation is applied. We consider chaos in a modified Li-Yorke sense such that infinitely many almost periodic motions take place in its basis. It is demonstrated that the system under investigation possesses countable infinity of chaotic sets of solutions. Coupled Duffing oscillators are used to show the effectiveness of our technique, and simulations that support the theoretical results are represented. Moreover, a chaos control procedure based on the Ott-Grebogi-Yorke algorithm is proposed to stabilize the unstable almost periodic motions embedded in the chaotic attractor.

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Chaos in economic models with exogenous shocks

Cited by 30 publications

References 37 publications

Exogenous Versus Endogenous for Chaotic Business Cycles

Exogenous Versus Endogenous for Chaotic Business Cycles

Chaos Control and Anticontrol of the Output Duopoly Competing Evolution Model

Persistence of Li–Yorke chaos in systems with relay

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