On the basis of our previous research, we deepen and complete a kind of macroeconomics IS-LM model with fractional-order calculus theory, which is a good reflection on the memory characteristics of economic variables, we also focus on the influence of the variables on the real system, and improve the analysis capabilities of the traditional economic models to suit the actual macroeconomic environment. The conditions of Hopf bifurcation in fractional-order system models are briefly demonstrated, and the fractional order when Hopf bifurcation occurs is calculated, showing the inherent complex dynamic characteristics of the system. With numerical simulation, bifurcation, strange attractor, limit cycle, waveform and other complex dynamic characteristics are given; and the order condition is obtained with respect to time. We find that the system order has an important influence on the running state of the system. The system has a periodic motion when the order meets the conditions of Hopf bifurcation; the fractional-order system gradually stabilizes with the change of the order and parameters while the corresponding integer-order system diverges. This study has certain significance to policymaking about macroeconomic regulation and control.
This paper investigates the problem of regret minimization for multi-armed bandit (MAB) problems with local differential privacy (LDP) guarantee. In stochastic bandit systems, the rewards may refer to the users' activities, which may involve private information and the users may not want the agent to know. However, in many cases, the agent needs to know these activities to provide better services such as recommendations and news feeds. To handle this dilemma, we adopt differential privacy and study the regret upper and lower bounds for MAB algorithms with a given LDP guarantee. In this paper, we prove a lower bound and propose algorithms whose regret upper bounds match the lower bound up to constant factors. Numerical experiments also confirm our conclusions.Preprint. Under review.
This paper examines the optimal decisions of dual-channel game model considering the inputs of retailing service. We analyze how adjustment speed of service inputs affect the system complexity and market performance, and explore the stability of the equilibrium points by parameter basin diagrams. And chaos control is realized by variable feedback method. The numerical simulation shows that complex behavior would trigger the system to become unstable, such as double period bifurcation and chaos. We measure the performances of the model in different periods by analyzing the variation of average profit index. The theoretical results show that the percentage share of the demand and cross-service coefficients have important influence on the stability of the system and its feasible basin of attraction.
Abstract:In this paper, a duopoly game model with double delays in hydropower market is established, and the research focus on the influence of time delay parameter on the complexity of the system. Firstly, we established a game model for the enterprises considering both the current and the historical output when making decisions. Secondly, the existence and stability of Hopf bifurcation are analyzed, and the conditions and main conclusions of Hopf bifurcation are given. Thirdly, numerical simulation and analysis are carried out to verify the conclusions of the theoretical analysis. The effect of delay parameter on the stability of the system is simulated by a bifurcation diagram, the Lyapunov exponent, and an entropic diagram; in addition, the stability region of the system is given by a 2D parameter bifurcation diagram and a 3D parameter bifurcation diagram. Finally, the method of delayed feedback control is used to control the chaotic system. The research results can provide a guideline for enterprise decision-making.
Based on the research of domestic and foreign scholars, this paper has improved and established a double oligopoly market model of renewable energy, and analyzed the complex dynamic characteristics of a system based on entropy theory and chaos theory, such as equilibrium point, stability, Hopf bifurcation conditions, etc. This paper also studied and simulated the effects of the natural growth rate of energy and the single delay decision on the renewable energy system by minimizing the entropy of the system and reducing the system instability to a minimum, so that the degree of disorder within the system was reduced. The results show that with the increase of the natural growth rate of energy, the stability of the system is not affected, but the market demand of the oligopoly 1 is gradually reducing and the market demand of the oligopoly 2 is gradually increasing. At the same time, a single oligopoly making the time delay decision will affect the stability of the two oligopolies. With the increase of delay, the time required to reach the stable state will grow, and the system will eventually enter the Hopf bifurcation, thus the system will have its entropy increased and fall into an unstable state. Therefore, in the actual market of renewable energy, oligopolies should pay attention to the natural growth rate of energy and time delay, ensuring the stability of the game process and the orderliness of the system.
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