A discrete fractional-order Cournot duopoly game

Xin, Baogui; Peng, Wei; Kwon, Yekyung

doi:10.1016/j.physa.2020.124993

Cited by 20 publications

(20 citation statements)

References 34 publications

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“…We know that the Beijing PM2.5 dataset originates from the nature field. In fact, we can try to employ the proposed AE-CNN-TL to predict a chaotic time series of medium-to-long term which comes from some artificial systems, such as the game system [19][20][21] and the financial system [22]. 8 Complexity…”

Section: Discussionmentioning

confidence: 99%

Prediction for Chaotic Time Series-Based AE-CNN and Transfer Learning

Xin

Peng

2020

Complexity

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It has been a hot and challenging topic to predict the chaotic time series in the medium-to-long term. We combine autoencoders and convolutional neural networks (AE-CNN) to capture the intrinsic certainty of chaotic time series. We utilize the transfer learning (TL) theory to improve the prediction performance in medium-to-long term. Thus, we develop a prediction scheme for chaotic time series-based AE-CNN and TL named AE-CNN-TL. Our experimental results show that the proposed AE-CNN-TL has much better prediction performance than any one of the following: AE-CNN, ARMA, and LSTM.

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Section: Discussionmentioning

confidence: 99%

Prediction for Chaotic Time Series-Based AE-CNN and Transfer Learning

Xin

Peng

2020

Complexity

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“…The fractional derivative of continuous-time real functions was defined and formulated by Liouville, Grunwald, Letnikov and Riemann in the late nineteenth century, but the first definition of the fractional difference operator was introduced by Diaz and Olser in 1974 [31]. The focus of mathematicians, biological mathematicians and economists has recently moved to direct application of fractional difference equations, which tend to be more directly applicable to the mathematical modeling of systems with memory [32][33][34][35][36][37][38][39][40]. Few studies have recently explored the dynamics of fractional forms for some traditional chaotic maps, as well as the study of control and synchronization in such fractional maps [38][39][40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

“…The focus of mathematicians, biological mathematicians and economists has recently moved to direct application of fractional difference equations, which tend to be more directly applicable to the mathematical modeling of systems with memory [32][33][34][35][36][37][38][39][40]. Few studies have recently explored the dynamics of fractional forms for some traditional chaotic maps, as well as the study of control and synchronization in such fractional maps [38][39][40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

On discrete fractional-order Lotka-Volterra model based on the Caputo difference discrete operator

Elsonbaty

Elsadany

2021

Math Sci

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This work aims at introducing a new discrete fractional order model based on Lotka-Volterra prey-predator model with logistic growth of prey species. The proposed model is a generalization of the standard integer order discrete-time Lotka-Volterra model to its fractional-order version while incorporating also logistic growth for prey population. The equilibrium points of the presented model are firstly obtained, and their stability analysis is conducted. Then, the nonlinear dynamics of the proposed model and possible occurrence of chaotic behavior are explored. The effects of fractional order along with other key parameters in the model are investigated using several techniques. Thorough numerical simulations are carried out where Lyapunov exponents, bifurcation diagrams, phase portraits and as well as C 0 complexity measure are obtained to analyze the dynamics of the proposed model and confirm theoretical results.

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“…The local stability properties of the equilibrium points are studied, along with the effects of the fractional marginal profit on the game dynamics [3]. In [17] a fractional-order discrete Cournot duopoly game model is introduced, which allows participants to make decisions while making full use of their historical information. The Nash equilibria, their local stability and the presence of chaos are deeply investigated [17].…”

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confidence: 99%

“…In [17] a fractional-order discrete Cournot duopoly game model is introduced, which allows participants to make decisions while making full use of their historical information. The Nash equilibria, their local stability and the presence of chaos are deeply investigated [17]. In [5] a discrete dynamic system that describes the competition among four firms is presented.…”

mentioning

confidence: 99%