Feedback Optimality Condition for Nonconvex Discrete Linear-Quadratic Optimal Control Problem

The paper analyzed a non-convex linear-quadratic optimization problem in a discrete dynamic system. We obtained necessary optimality condition with feedback controls which allow a descent of the functional cost. Such controls are generated by the quadratic majorant of the cost. In contrast to the discrete maximum principle, this condition does not require any convexity properties of the problem.

Exploring the Quantity Change Pattern of Environment-Friendly Products in the Sharing Economy

In the practice of various Internet-based sharing economies, environmental issues of shared products become more prominent and urgent. By analysing the relationship among government, enterprises, and consumers, this paper develops a system dynamics model based on the evolutionary game theory to explore the quantity change pattern of environment-friendly products in a sharing industry. A discrete dynamic system simulation of the quantity change process takes shared bikes in Beijing as a case study. The simulation results are consistent with the analysis of evolutionary game theory. The results show that government subsidies to both enterprises and consumers can lead to higher quantities of environment-friendly shared products, while consumer subsidy is better than enterprise subsidy. In addition, governments and enterprises need to ensure moderate investments to improve consumer experience and environmental awareness.

Discrete Optimization on Train Rescheduling on Single-Track Railway: Clustering Hierarchy and Heuristic Search

This paper focuses on discrete dynamic optimization on train rescheduling on single-track railway with the consideration of train punctuality and station satisfaction degree. A discrete dynamic system is firstly described to mimic train rescheduling, and a state transition function is specially designed according to the train departure event. The purpose of this function is to improve simulation efficiency by directly confirming the next discrete time. After the construction and analysis of optimization models to discrete dynamic system, a two-stage heuristic search strategy is developed, by using clustering hierarchy theory and stochastic search strategy, to obtain train departure time and arrival time before each state transition of the system. Finally, a numerical experiment is conducted to verify the proposed system, models, and the heuristic search strategy. The result shows that the discrete dynamic system, together with the state transition function and heuristic search strategy, shows better performance in simulation efficiency and solution quality.

Susceptible-Infected-Susceptible Epidemic Discrete Dynamic System Based on Tsallis Entropy

This investigation deals with a discrete dynamic system of susceptible-infected-susceptible epidemic (SISE) using the Tsallis entropy. We investigate the positive and maximal solutions of the system. Stability and equilibrium are studied. Moreover, based on the Tsallis entropy, we shall formulate a new design for the basic reproductive ratio. Finally, we apply the results on live data regarding COVID-19.

Research on Discrete Dynamic Forecasting Model of Government Human Resources

For the evolution of complex system, especially the unbalanced complex system, dynamic is its universal attribute. In this paper, by introducing the discrete dynamic system model in complex system research, a method of establishing the discrete dynamic system model of government human resources system is proposed from the vertical level. In this study, human resources were forecasted by the method of manpower/population ratio, linear regression and grey system, and the total number of health human resources in A city from 2018 to 2022 was forecasted by weighted average combination method. The results show that we should make great efforts to innovate the training mode of health personnel, improve the enthusiasm of staff, and reasonably control the expansion of hospitals.

Price Discrimination in Dynamic Cournot Competition

This paper introduces a new Cournot duopoly game and gives an applied study for price discrimination in a market by dynamic methods. One of two oligopolies has two different prices for a homogeneous product, while the other charges one kind of price. It is found that there is only one stable equilibrium for the discrete dynamic system, and a corresponding stable condition is given. Using a discriminative price is not always beneficial to a firm in equilibrium. If both oligopolies carry out price discrimination, the market’s average price is lower than when only one oligopoly does it. The results are verified by numerical simulations.

RECURRENT REPRESENTATION FOR NON-STATIONARY PARAMETER ESTIMATE OF LEAST SQUARES METHOD WITH LEAST DEVIATIONS FROM "ATTRACTION" POINTS FOR BILINEAR DYNAMIC SYSTEMS

The estimation problem of non-stationary parameter matrices is considered for bilinear discrete dynamic system in the case when for these unknown parameter matrices their ‘attraction’ points are known at any moment. Explicit and recurrent forms of representation are obtained for these parameter estimates of the least squares method with variable forgetting factor and least deviation norm from ‘attraction’ points under non-classical assumptions. The recurrent algorithm is also proposed for corresponding weighted residual sum of squares.

A study of stability and bifurcation analysis in discrete-time predator–prey system involving the Allee effect

This paper deals with a discrete-time predator–prey system which is subject to an Allee effect on prey. We investigate the existence and uniqueness and find parametric conditions for local asymptotic stability of fixed points of the discrete dynamic system. Moreover, using bifurcation theory, it is shown that the system undergoes Neimark–Sacker bifurcation in a small neighborhood of the unique positive fixed point and an invariant circle will appear. Then the direction of bifurcation is given. Furthermore, numerical analysis is provided to illustrate the theoretical discussions with the help of Matlab packages. Thus, the main theoretical results are supported with numerical simulations.