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Abstract Objective To compare the outcomes of patients undergoing Retroperitoneal laparoscopic Radical nephrectomy (RLRN) and Transperitoneal laparoscopic Radical nephrectomy (TLRN). Methods A total of 120 patients with localized renal cell carcinoma were randomized into either RLRN or TLRN group. Mainly by comparing the patient perioperative related data, surgical specimen integrity, pathological results and tumor results. Results Each group comprised 60 patients. The two group were equivalent in terms of perioperative and pathological outcomes. The mean integrity score was significantly lower in the RLRN group than TLRN group. With a median follow-up of 36.4 months after the operation, Kaplan–Meier survival analysis showed no significant difference between RLRN and TLRN in overall survival (89.8% vs. 88.5%; P = 0.898), recurrence-free survival (77.9% vs. 87.7%; P = 0.180), and cancer-specific survival (91.4% vs. 98.3%; P = 0.153). In clinical T2 subgroup, the recurrence rate and recurrence-free survival in the RLRN group was significantly worse than that in the TLRN group (43.2% vs. 76.7%, P = 0.046). Univariate and multivariate COX regression analysis showed that RLRN (HR: 3.35; 95%CI: 1.12–10.03; P = 0.030), male (HR: 4.01; 95%CI: 1.07–14.99; P = 0.039) and tumor size (HR: 1.23; 95%CI: 1.01–1.51; P = 0.042) were independent risk factor for recurrence-free survival. Conclusions Our study showed that although RLRN versus TLRN had roughly similar efficacy, TLRN outperformed RLRN in terms of surgical specimen integrity. TLRN was also significantly better than RLRN in controlling tumor recurrence for clinical T2 and above cases. Trial registration Chinese Clinical Trial Registry ( https://www.chictr.org.cn/showproj.html?proj=24400 ), identifier: ChiCTR1800014431, date: 13/01/2018.

Advertising and sales promotion are two important specific marketing communications tools. In this paper, nonlinear differential equation and single parameter sales promotion strategy are introduced into an advertising model and investigated quantitatively. The existence and stability of period-nT (n = 1, 2, 4, 8) solutions are investigated. Interestingly, both period doubling bifurcation and inverse flip bifurcation occur at different parameter values in the same advertising model. The results show that the system enters into chaos from stable state through flip bifurcation and enters into stable state from chaos through inverse flip bifurcation. An effective control strategy, which suppresses flip bifurcation and promotes inverse flip bifurcation, is proposed to eliminate chaos. These results have some significant theoretical and practical value in related markets.

Motivated by the electric vehicle battery life performance, we studied the optimal investment decision-making behaviour of duopoly automakers. Based on the framework of game theory, this paper explores the influence of various parameters in the static game and dynamic game on the results, in combination with consumers’ preference for the battery life of electric vehicles. In the static game, a smaller investment coefficient is more beneficial to a firm that adopts an investment strategy rather than a firm that does not. When the investment coefficient increases, the difference between the two manufacturers will become smaller. The change of parameters in the dynamic game system may lead to complex dynamic phenomena, and the system will experience period-doubling bifurcation and N-S bifurcation from a stable state into a chaotic state. It will also significantly impact the basins of attraction, which affect the decision-makers’ initial choice. Consequently, we can use the control method to return the unstable system to stability. Based on these findings, some management insights and suggestions are presented.

The whole world has entered the era of the Vuca. Some traditional methods of problem analysis begin to fail. Complexity science is needed to study and solve problems from the perspective of complex systems. As a complex system full of volatility and uncertainty, price fluctuations have attracted wide attention from researchers. Therefore, through a literature review, this paper analyzes the research on complex theories on price prediction. The following conclusions are drawn: (1) The price forecast receives widespread attention year by year, and the number of published articles also shows a rapid rising trend. (2) The hybrid model can achieve higher prediction accuracy than the single model. (3) The complexity of models is increasing. In the future, the more complex methods will be applied to price forecast, including AI technologies such as LLM. (4) Crude-oil prices and stock prices will continue to be the focus of research, with carbon prices, gold prices, Bitcoin, and others becoming new research hotspots. The innovation of this research mainly includes the following three aspects: (1) The whole analysis of all the articles on price prediction using mathematical models in the past 10 years rather than the analysis of a single field such as oil price or stock price. (2) Classify the research methods of price forecasting in different fields, and found the common problems of price forecasting in different fields (including data processing methods and model selection, etc.), which provide references for different researchers to select price forecasting models. (3) Use VOSviewer to analyze the hot words appearing in recent years according to the timeline, find the research trend, and provide references for researchers to choose the future research direction.

Diseases, natural disasters, and other emergencies force the economy and management system to confront nonlinear and random changes. In recent years, complexity science has attracted much attention. Complex economics believes that economic models are dynamic, stochastic, and unpredictable, and that equilibrium and stability are temporary. It is changing traditional economic theory. Based on complexity theory, bibliometric theory, nonlinear theory, and game theory, combined with knowledge graph methods, the article analyzed 200 papers from the Web of Science, covering the period 1998–2022. This research presents the research structure and theoretical evolution of complex economic games through visualization techniques. The clusters of keywords and the logical relationships between them are discussed. Then, the analysis of hot keywords and co-occurrence keywords is carried out. Finally, future research directions for complex economic games are given: (1) the market complexity that comes with intelligent expectations, (2) complex characteristics of the data trading market, and (3) complex risk control for emergencies. The innovation lies in the use of data analysis software combined with manual knowledge to overcome the shortcomings of inflexible software analysis, as well as weak manual storage and computation. This research builds a theoretical foundation for grasping the research direction and selecting advanced topics.

In this paper, based on chaos theory and dynamic system simulation, a dynamic model of a relational leadership system with pressure factors is established and simulated. The study found that the excessive self-leadership and the relational leadership cannot effectively improve the leadership effectiveness of leaders. In addition, with the adjustment of the self-leadership adjustment coefficient, leadership effectiveness will change from a stable state to a chaotic state. Only by adopting limited rational decision-making strategies in multicycle decision-making can leaders maintain a high level of leadership effectiveness. Previous research mainly focuses on the theoretical analysis of the complexity of the leadership system or the issuance of questionnaires, but seldom on the dynamic complex process of the leadership system. This study reveals the complexity and chaos characteristics of the dynamic evolution of the multifactor relational leadership system, puts forward the relational leadership theory and the complex leadership theory under the influence of pressure, and makes some suggestions on how to improve the leadership effectiveness under the complex environment. The research results are of great significance to theoretical innovation and practical application.

We consider a Cournot game model between an OEM (original equipment manufacturer) and an IR (independent remanufacturer). The OEM manufactures new products and decides the quality level. IR remanufactures and obtains OEM’s technology through technology licensing or joint R&D. To prevent the cannibalization of new products by remanufactured products, the OEM may be reluctant to disclose latest technology to the IR. When the IR chooses the technology licensing mechanism, it will be in a rather disadvantaged position in the competition. In contrast, joint R&D can avoid this dilemma. The two mechanisms are comparatively analyzed under static equilibrium and complex dynamics from three aspects: (1) the output of new and remanufactured products, (2) the profits of the OEM and the IR, and (3) TEI (total environmental impact) under technology licensing mechanism and joint R&D mechanism, respectively. Based on the theoretical and numerical analysis, we derive that the joint R&D mechanism can achieve a Pareto improvement over the royalty mechanism under certain conditions. The stability, bifurcation, chaos, and largest Lyapunov exponent are analyzed in the dynamic model. Numerical examples show that chaos may cause the OEM and the IR to lose profits or even be in deficit. But from the perspective of TEI, chaos can be beneficial. Interestingly, some conclusions in the static setting are reversed in the chaotic state. We propose a feedback adjustment method to eliminate chaos.

Nowadays, with a great number of household electrical appliances being discarded in every corner of the world every day, household electrical appliances recycling is attracting more attention. In this paper, we build a closed-loop supply chain that consists of a manufacturer and a third-party recycler based on the development of “Internet Plus” recovery platform. We thoroughly analyze the model and its evolution by chaos theory, complex dynamics theory, and numerical simulation and introduce the adaptive method to control the chaos of the system. We find that as the manufacturer increases the retail price, the stable area of the market becomes smaller. At the same time, when the manufacturers direct recycle price or the price adjustment range of the products recycled from the third party exceeds a certain threshold, all the recycle prices in the whole market will fluctuate, thus causing market chaos. Among them, as an adjustment decision method, delay strategy reduces the volatility of recycle price and makes it return to a stable state, which is an effective method to control system disorder. In addition, the third-party recycler will change the optimal subsidy model according to the government’s price subsidy level, while the manufacturer always prefers the price subsidy model.

Nowadays, with global scientific and technological levels rapidly improving, innovation has been a great need for enterprises to solve the dilemma. Combined with EPR (Extended Producer Responsibility) and the topic of remanufacturer, adopting green innovation has been an effective way when green supply chain management is applied. In this paper, we focus on the activity of green innovation and build a model where the manufacturer will invest in green innovation to improve the product availability rate of recycled products and save the cost in the process of remanufacturing. Besides, we take three stages in a cycle into consideration, that is, production/sale, recycling used production, and remanufacture/sale, and meanwhile, the government gives a subsidy to enterprises to encourage the activity of recycling. In the process of model solving, we take a dynamic decision-making way into consideration. We find that the decision adjustment speed of players has a significant effect on the stability, and in a long dynamic repeated game process, with the speed of decision adjustment increasing, the system enters into chaos at the end of the process. It is interesting that when the speed of decision adjustment exceeds the critical point of the bifurcation diagram, the profit of the manufacturer decreases and then enters a chaotic state. Besides, with the level of subsidies increasing, the area of stable region decreases gradually. Certain investment has a positive effect on product selling and recycling as well as the profit, and the government subsidy undoubtedly raises the profit of manufacturers and encourages the activity of recycling. In the end, we make chaos control by adjusting the decision method.

Internet of Things is the core technology of smart agriculture and can reform and upgrade traditional agriculture for reducing cost, reducing pollution, and increasing productivity and quality in China. From government-led and market economy perspectives, promotion mechanisms and sustainable adoption of agricultural Internet of Things technology are analyzed. In the initial application phase, the promotion of Internet of Things requires government support. For investigating the relationship between the government and farmers, this study builds an evolutionary game model and finds that increases of cost subsidy, farmers’ negative feedback, government’s positive feedback, and chemical agriculture cost can make the model evolve toward the strategy set: farmer adoption and government support. For long-term development, a sustainable model in competitive market is built by competition game and exponential replication equation. This paper analyzes the equilibrium of adoption ratio, long-run profit, and the conversion between equilibrium points under capacity sharing strategy in competitive market. It is also found that the market will eventually evolve to the technology selection strategy whose long-run average profit dominates the market. The innovations are that evolutionary game is used for analyzing the initial stage and competitive game and asynchronous update mechanism are used for analyzing the sustainable development adoption. At last, references are provided for agricultural Internet of Things development policy from the perspectives of initial promotion and long-run sustainability.

Nowadays, with more and more people choosing energy-saving product, green supply chain is increasingly becoming popular. In this paper, we build a dynamic Stackelberg game model that contains government, two green innovation enterprise which is a leader and produces two kinds of green product with similar function but different quality and a retailer selling two kinds of green product meanwhile. We use classical backward induction to solve the model. Price decision is considered first and is divided into two stages. We analyze the equilibrium price of green innovation enterprise and retailer and the stable region. Next, we analyze energy-saving index of two kinds of green product. Through numerical simulation, we further analyze system's stability conditions and system's dynamic evolution process when different parameter is adopted. In the end, we consider green products’ baseline energy-saving index made by government and get the optimal baseline energy-saving index by numerical simulation. We find that too stringent subsidy standards may can't induce manufacturer to invest greener technology. Besides, we use the delay feedback control to effectively control the chaotic phenomenon. Keywords: Green innovative enterprise, Governmental policy making, Game theory, Complex system

In this paper, two noncooperative dynamic pricing strategies are used in a supply chain. Two dynamic Stackelberg game models have been built involving both a manufacturer and a retailer assumed to be the leader in order. In the two models, the manufacturer sells national-brand (NB) product to an independent retailer or directly to consumers through a direct channel. The retailers sell a store-brand (SB) product when they sell the NB product coming from the manufacturer. Thus, there is competition both in different channels and in products with different brands. To analyze the complexity of the model, parameter bifurcation diagrams and strange attractor diagrams have been therefore plotted. The results show that the game leader has advantages when the market is stable, but it turns disadvantageous if the state falls into unstable as the game follower can quickly adjust the strategy to seize the market. The wholesale price and the direct selling price are high that they incur larger profits if the manufacturer is dominant, but it gets worse when the adjustment speed increases. While in the model where the retailer plays a dominant role, the increase in the adjustment speed is unfavorable to retailer. By controlling the total cost of the direct channel and increasing channel competition strength and brand competition strength, the manufacturers can increase their profits in the game dominated by the retailer. In addition, the stable region within the system will be narrow since the market is sensitive to the channel competition, brand competition, and advertising indifference.

Based on the thinking of holism and reductionism, this paper creatively constructed the credit asset pricing model of enterprises’ accounts receivable, namely, the BEST pricing model, and it was demonstrated effectively. The model gave an overall evaluation on the default probability of buyer and environment, as well as buyer loss given default resulting from the factors including Seller (S), Buyer (B), and Environment (E). The model is also utilized with the optimal control management Technology (T) to maximize the intrinsic value of the credit asset. The paper put forward the Duration of accounts receivable aging, measurement method of dynamic free interest rate, and amended the KMV model to solve the default probability of accounts receivable of listed and nonlisted companies. To evaluate the credit asset risk, the following were selected: three effective financial indicators, seven nonfinancial index clusters, and sixty-three specific nonfinancial index variables of the buyer; one index and eight specific indicators of the seller; and one index and fourteen specific indicators of nonsystematic risk of the environment. Five appropriate hedge parameters are used to control the risk.

According to game theory, chaotic dynamics theory, and complexity based on the literature review about the pricing strategy and recycling channels of the closed-loop supply chain, on the background of the widespread hybrid recycling channels in Chinese electronic products market, this paper builds a closed-loop supply chain model with dual-channel recycling composed of one manufacturer and one third-party. We assume that the consumer perception towards the remanufacturing products is uncertain and limited. We carry on theoretical analysis of this model and perform numerical simulations from the perspective of entropy theory. Results show that a precipitous speed of recycling price adjustment of the manufacturer or the third-party will both lead the system into a chaotic state and cause the entropy of the system to increase. The system is sensitive to initial conditions in this chaotic condition. Focusing on the harmful effects of chaotic system, we introduce adjustment parameter to efficiently control the chaos. The results have a strong reference value to practical problems, so it has a great value in both theory and application.

Based on the real situation of telecom industry in China, we establish a triopoly game model, which includes two competitive telecom firms and their correlative corporation which produces the complementary product. Both free market and bundling market will be concerned in this dynamic model. Moreover, we consider a one-to-many bundling way instead of two complementary products in terms of the proportion of one to one in a bundling product. By numerical simulation, we find that stable space will decrease and decision chaos appears when the degree of the competition becomes fierce between the two competitive telecom firms. Besides, increasing the amount of bundling services provided by a telecom firm can lead to different impacts on the prices of the three firms investigated. This paper enriches the decision-making for the strategy of bundling pricing and will be valuable for the telecom operators.

Advertising and sales promotion are two important specific marketing communications tools. In this paper, Internet sales promotion is introduced into a differential advertising model and investigated quantitatively. The conditions for the existence and stability of periodic solutions are obtained. Flip bifurcation of periodic solution is investigated analytically. The results show that the sales promotion parameter can modify the stability of the differential advertising model and lead to chaos through flip bifurcation, the sales level will eventually be no less than a given value by adjusting the value of the sales promotion parameter, and the optimal sales promotion strategy can lead to maximum profit. Numerical results for periodic solutions, bifurcation diagrams, and the effects of sales promotion strategies, which are illustrated with an example, are in good agreement with the theoretical analysis. These results have certain significant theoretical and practical value in related markets.

We establish in this paper a new two-stage supply chain with one manufacturer and two retailers which have a fixed market share in the mature and stable market with specific reference to consumer electronics industry. This paper offers insights into how the three forecasting methods affect the bullwhip effect considering the market share under the ARMA(1,1) demand process and the order-up-to inventory policy. We also discuss the stability of the order with the theory of entropy. In particular, we derive the expressions of bullwhip effect measure under the MMSE, MA, and ES methods and compare them by numerical simulations. Results show that the MA is always better in contrast to the ES for reducing the bullwhip effect in our supply chain model. When moving average coefficient is lower than a certain value, the MMSE method is the best for reducing the bullwhip effect; otherwise, the MA method is the best. Moreover, the larger the market share of the retailer with a long lead time is, the greater the bullwhip effect is, no matter what the forecasting method is.

At present, most of the manufacturers are increasingly laying emphasis on dual-channel selling. The level of consumer’s preference is diverse with different channels. This study discusses a supply chain where one common manufacturer uses two different channels to sell product. The bounded rationality expectation has been applied to explore the decision-making mechanism in finalizing the wholesale prices and sales commissions for the manufacturer and retailers. In addition, the dynamic features of the system are simulated by 2D bifurcation diagram, the largest Lyapunov exponent, attractor variation, and time series. The simulation results suggest that if the adjustment speeds of the wholesale prices and sales commissions change drastically, the system would fall into a chaotic state. If the consumers prefer the online channel, the wholesale prices and sales commissions may be raised and vice versa. However, too strong preference of each channel will make the system appear to have a considerably periodic fluctuation, even chaos. In the meantime, the parameter adjustment method can help make the periodic or chaotic system go back to stability. Therefore, the significance of this study is with a practical meaning to make better pricing strategy for players in dual-channel selling supply chain system.

With the purpose of researching the bullwhip effect when there is a callback center in the supply chain system, this paper establishes a new supply chain model with callback structure, which has a material supplier, a manufacture, and two retailers. The manufacture and retailers all employ AR(1) demand processes and use order-up-to inventory policy when they make order decisions. Moving average forecasting method is used to measure the bullwhip effect of each retailer and manufacture. We investigate the impact of lead-times of retailers and manufacture, forecasting precision, callback index, and marketing share on the bullwhip effect of both retailers and manufacture. Then we use the method of numerical simulation to indicate the different parameters in this supply chain. Furthermore, this paper puts forward some suggestions to help the enterprises to control the bullwhip effect in the supply chain with callback structure.

Analysis of the characteristics of agricultural product price volatility and trend forecasting are necessary to formulate and implement agricultural price control policies. Taking wholesale cabbage prices as an example, a multiple test methodology has been adopted to identify the nonlinearity, fractality, and chaos of the data. The approaches used include the R/S analysis, the BDS test, the power spectra, the recurrence plot, the largest Lyapunov exponent, the Kolmogorov entropy, and the correlation dimension. The results show that there is chaos in agricultural wholesale price data, which provides a good theoretical basis for selecting reasonable forecasting models as prediction techniques based on chaos theory can be applied to forecasting agricultural prices.

This paper studies the complex characteristics caused by the price competition in multichannel household appliance supply chains. We consider a two-level household appliance supply chain system consisting of a manufacturer with an Internet channel and a retailer with a traditional channel and an Internet channel. Each channel’s price-setting follows the bounded rational decision process in order to obtain the optimal profit or more market share. Considering that the price competition often leads to the demand and order fluctuation, we also investigate the bullwhip effect of the multichannel supply chains on the basis of the order-up-to-inventory policy. From the numerical simulation, we find a system in a chaotic state will suffer larger bullwhip effect than a stable system, and the manufacturer’s Internet channel is helpful to mitigate the bullwhip effect. Our results provide some useful managerial inspirations for the household manufacturer and retailers. Firstly, each channel should make their retail price with a suitable price adjustment speed in the stable region, and each time pricing cannot exceed the domain of attraction. Secondly, the manufacturer can adopt a more radical pricing strategy in their Internet channel to mitigate the bullwhip effect. Thirdly, the price adjustment should be reviewed and be appropriately reduced if the price adjustment is too large.

Apart from the price fluctuation, the retailers’ service level becomes another key factor that affects the market demand. This paper depicts a modified price and demand game model based on the stochastic demand and the retailer’s service level which influences the market demand decided by customers’ preference, while the market demand is stochastic in this model. We explore how the price adjustment speed affects the stability of the supply chain system with respect to service level and stochastic demand. The dynamic behavior of the system is researched by simulation and the stability domain and the bifurcation phenomenon are shown clearly. The largest Lyapunov exponent and the chaotic attractor are also given to confirm the chaotic characteristic of the system. The simulation results indicate that relatively small price adjustment speed may maintain the system at stable state. With the price adjustment speed gradually increasing, the price system gets unstable and finally becomes chaotic. This chaotic phenomenon will perturb the product market and this phenomenon should be controlled to keep the system stay in the stable region. So the chaos control is done and the chaos can be controlled completely. The conclusion makes significant contribution to the system referring to the price fluctuation based on the service level and stochastic demand.

This paper studies internal reference price effects when competitive firms face reference price effects and make decisions based on partial information, where their decision-making mechanism is modeled by a dynamic adjustment process. It is shown that the evolution of this dynamic adjustment goes to stabilization if both adjustment speeds are small and the complexity of this evolution increases in adjustment speeds. It is proved that the necessary condition for flip bifurcation or Neimark-Sacker bifurcation will occur with the increase of adjustment speed in two special cases. What is more, numerical simulations show that these bifurcations do occur. Then, the impacts of parameters on stability and profits are investigated and some management insights for firms with limited information to take advantage of reference price effects are provided.

This paper considers price as a strategy using two methods of market segmentation through game theory based on the collected data of several typical cities in Shandong province. Three oligarchs are discussed to analyze the complexity of the market in tobacco system. The effect of different factors on the equilibrium price of Nash equilibrium is discussed. What is more, the variation of parameters drives the system to change to uncertain status, even to bifurcation or chaos. We also discuss the model under normal circumstances, when the three parties jointly take chaos control measures, and its impact on the system. Finally, we clarify chaos control of economic significance. The results indicate that only reasonable pricing strategy is a critical point to achieve maximized profit and maintain orderly operation at the same time, which is a constructive suggestion for tobacco companies’ operational strategy.

The impact of inaccurate demand beliefs on dynamics of a Triopoly game is studied. We suppose that all the players make their own estimations on possible demand with errors. A dynamic Triopoly game with such demand belief is set up. Based on this model, existence and local stable region of the equilibriums are investigated by 3D stable regions of Nash equilibrium point. The complex dynamics, such as bifurcation scenarios and route to chaos, are displayed in 2D bifurcation diagrams, in which e1 and α are negatively related to each other. Basins of attraction are investigated and we found that the attraction domain becomes smaller with the increase in price modification speed, which indicates that all the players’ output must be kept within a certain range so as to keep the system stable. Feedback control method is used to keep the system at an equilibrium state.

In this paper, we study a supply chain system which consists of one manufacturer and two retailers including a traditional retailer and an online retailer. In order to gain a larger market share, the retailers often take the sales as a decision-making variable in the competition game. We devote ourselves to analyze the bullwhip effect in the supply chain with sales game and consumer returns via the theory of entropy and complexity and take the delayed feedback control method to control the system’s chaotic state. The impact of a statutory 7-day no reason for return policy for online retailers is also investigated. The bounded rational expectation is adopt to forecast the future demand in the sales game system with weak noise. Our results show that high return rates will hurt the profits of both the retailers and the adjustment speed of the bounded rational sales expectation has an important impact on the bullwhip effect. There is a stable area for retailers where the bullwhip effect doesn’t appear. The supply chain system suffers a great bullwhip effect in the quasi-periodic state and the quasi-chaotic state. The purpose of chaos control on the sales game can be achieved and the bullwhip effect would be effectively mitigated by using the delayed feedback control method.

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.

We construct dynamic Bertrand-Stackelberg pricing models including two manufacturers and a common retailer in a risk-averse supply chain with the uncertain demand. The risk-averse supply chain follows these strategies: Bertrand game between the two manufacturers and Stackelberg game between the manufacturer and the retailer. We study the effect of the price adjustment speed, the risk preference, and the uncertain demand on the stability of the risk-averse supply chain using bifurcation, power spectrum, attractor, and so forth. It is observed that there exists slip bifurcation when the price adjustment speed across some critical value, the stable region, and total profit of the risk-averse supply chain will increase with increase of RM1 and decrease with increase of σ. The profit of the supply chain and the two manufacturers will decrease and the weaker (retailer) is a beneficiary when the supply chain is in chaos. The fluctuation in the supply chain can be gradually controlled by the control of the price adjustment speed.

This paper studied system dynamics characteristics of closed-loop supply chain using repeated game theory and complex system theory. It established decentralized decision-making game model and centralized decision-making game model and then established and analyzed the corresponding continuity system. Drew the region local stability of Nash equilibrium and Stackelberg equilibrium, and a series of chaotic system characteristics, have an detail analysis of the Lyapunov index which is under the condition of different parameter combination. According to the limited rational expectations theory, it established repeated game model based on collection price and marginal profits. Further, this paper analyzed the influence of the parameters by numerical simulations and concluded three conclusions. First, when the collection price is to a critical value, the system will be into chaos state. Second, when the sale price of remanufacturing products is more than a critical value, the system will be in chaos state. Last, the initial value of the collection price is sensitive, small changes may cause fluctuations of market price. These conclusions guide enterprises in making the best decisions in each phase to achieve maximize profits.

We establish a master-slave oligopoly game model with an upstream monopoly whose output is considered and two downstream oligopolies whose prices are considered. The existence and the local stable region of the Nash equilibrium point are investigated. The complex dynamic properties, such as bifurcation and chaos, are analyzed using bifurcation diagrams, the largest Lyapunov exponent diagrams, and the strange attractor graph. We further analyze the long-run average profit of the three firms and find that they are all optimal in the stable region. In addition, delay feedback control method and limiter control method are used in nondelayed model to control chaos. Furthermore, a delayed master-slave oligopoly game model is considered, and the three firms’ profit in various conditions is analyzed. We find that suitable delayed parameters are important for eliminating chaos and maximizing the profit of the players.

Although oligopoly theory is generally concerned with the single-product firm, what is true in the real word is that most of the firms offer multiproducts rather than single products in order to obtain cost-saving advantages, cater for the diversity of consumer tastes, and provide a barrier to entry. We develop a dynamical multiproduct Cournot duopoly model in discrete time, where each firm has an owner who delegates the output decision to a manager. The principle of decision-making is bounded rational. And each firm has a nonlinear total cost function due to the multiproduct framework. The Cournot Nash equilibrium and the local stability are investigated. The tangential bifurcation and intermittent chaos are reported by numerical simulations. The results show that high output adjustment speed can lead to output fluctuations which are characterized by phases of low volatility with small output changes and phases of high volatility with large output changes. The intermittent route to chaos of Flip bifurcation and another intermittent route of Flip bifurcation which contains Hopf bifurcation can exist in the system. The study can improve our understanding of intermittent chaos frequently observed in oligopoly economy.

This paper studied some realistic recycle fields at present in China, such as some daily machinery and equipment, electronic products, and plastic products. Under such circumstance, three oligarch retailers are a common situation. In this paper, we model and analyze the game of three oligarch retailers in a closed-loop supply chain. The stability of the Nash equilibrium, the bifurcation and chaos phenomenon of the recycling price and new product quantity when retailers change its adjustment speed, the profit trends of the three retailers, and the power spectrum are studied. At last, we used the parameter adjustment and the variable state feedback control strategy for chaos control, and the chaos of the system is delayed effectively. For closed-loop supply chain research, the conclusions of the numerical simulation in this paper not only have realistic guiding significance, but also have theoretical reference value.

An important phenomenon in supply chain management which is known as the bullwhip effect suggests that demand variability increases as one moves up a supply chain. This paper contrasts the bullwhip effect for a two-stage supply chain consisting of one supplier and two retailers under three forecasting methods based on the market share. We can quantify the correlation coefficient between the two retailers clearly, in consideration of market share. The two retailers both employ the order-up-to inventory policy for replenishments. The bullwhip effect is measured, respectively, under the minimum mean squared error (MMSE), moving average (MA), and exponential smoothing (ES) forecasting methods. The effect of autoregressive coefficient, lead time, and the market share on a bullwhip effect measure is investigated by using algebraic analysis and numerical simulation. And the comparison of the bullwhip effect under three forecasting methods is conducted. The conclusion suggests that different forecasting methods and various parameters lead to different bullwhip effects. Hence, the corresponding forecasting method should be chosen by the managers under different parameters in practice.

In this paper, setting the high-tech industry as the background, we build a dynamic duopoly game model in two cases with different government subsidies based on the innovation inputs and outputs, respectively. We analyze the equilibrium solution and stability conditions of the system, and study the dynamic evolution of the system under the conditions of different system parameters by the numerical simulation method. The simulation results show that both innovation subsidy policies have positive effects on firms’ innovation activities. Besides, improving the level of innovation can encourage firms to innovate. It also shows that an exaggerated adjusting speed of innovation outputs may cause complicated dynamic phenomena such as bifurcation and chaos, which means that the system has relatively higher entropy than that in a stable state. The degree of the government innovation subsidies is also shown to impact the stability and entropy of the system.

In this research, a model is established to represent a supply chain, which consists of one manufacturer and two retailers. The price-sensitive demand model is considered and the price game system is built according to the rule of bounded rationality as well as the entropy theory. With the increase of the price adjustment speed, the game system may go into chaos from the stable and periodic state. The bullwhip effect and inventory variance ratio of different stages that the system falls in are compared in real time. We also employ the delayed feedback control method to control the system and succeed in mitigating the bullwhip effect of the system. On the whole, the bullwhip effect and inventory variance ratio in the stable state are smaller than those in period-doubling and chaos. In the stable state, there is an optimal price adjustment speed to obtain both the lowest bullwhip effect and inventory variance ratio.

We examine the impact of three forecasting methods on the bullwhip effect in a two-stage supply chain with one supplier and two retailers. A first order mixed autoregressive-moving average model (ARMA(1, 1)) performs the demand forecast and an order-up-to inventory policy characterizes the inventory decision. The bullwhip effect is measured, respectively, under the minimum mean-squared error (MMSE), moving average (MA), and exponential smoothing (ES) forecasting techniques. The effect of parameters on the bullwhip effect under three forecasting methods is analyzed and the bullwhip effect under three forecasting methods is compared. Conclusions indicate that different forecasting methods lead to different bullwhip effects caused by lead time, underlying parameters of the demand process, market competition, and the consistency of demand volatility between two retailers. Moreover, some suggestions are present to help managers to select the forecasting method that yields the lowest bullwhip effect.

A Cournot-Bertrand mixed duopoly game model is constructed. The existence and local stable region of the Nash equilibria point are investigated. Complex dynamic properties such as bifurcation and route to chaos are analyzed using parameter basin plots. The strange attractors are also studied when the system is in chaotic states. Furthermore, considering the memory of the market, a delayed Cournot-Bertrand mixed model is considered and the results show that the delayed system has the same Nash equilibrium and has a higher chance of reaching steady states or cycles than the model without delay. So making full use of the historical data can improve the system’s stability.

A Cournot-Bertrand mixed duopoly game model with limited information about the market and opponent is considered, where the market has linear demand and two firms have the same fixed marginal cost. The principles of decision-making are bounded rational. One firm chooses output and the other chooses price as decision variable, with the assumption that there is a certain degree of differentiation between the products offered by firms to avoid the whole market being occupied by the one that applies a lower price. The existence of Nash equilibrium point and its local stability of the game are investigated. The complex dynamics, such as bifurcation scenarios and route to chaos, are displayed using parameter basin plots by numerical experiment. The influences of the parameters on the system performance are discussed from the perspective of economics.

A hyperchaotic system is introduced, and the complex dynamical behaviors of such system are investigated by means of numerical simulations. The bifurcation diagrams, Lyapunov exponents, hyperchaotic attractors, the power spectrums, and time charts are mapped out through the theory analysis and dynamic simulations. The chaotic and hyper-chaotic attractors exist and alter over a wide range of parameters according to the variety of Lyapunov exponents and bifurcation diagrams. Furthermore, linear feedback controllers are designed for stabilizing the hyperchaos to the unstable equilibrium points; thus, we achieve the goal of a second control which is more useful in application.

Based on the traditional IS–LM economic theory, which shows the relationship between interest rates and output in the goods and services market and the money market in macroeconomic. We established a four-dimensional IS–LM model involving four variables. With the Caputo fractional calculus theory, we improved it into a fractional order nonlinear model, analyzed the complexity and stability of the fractional order system. The existences conditions of attractors under different order conditions are compared, and obtain the orders when the system reaches a stable state. Have the detail analysis on the dynamic phenomena, such as the strange attractor, sensitivity to initial values through phase diagram and the power spectral. The order changes in two ways: orders changes synchronously or single order changes. The results show regardless of which the order situation is, the economic system will enter into multiple states, such as strong divergence, strange attractor and the convergence, finally, system will enter into the stable state under a certain order; parameter changes have similar effects on the economic system. Therefore, selecting an appropriate order is significant for an economic system, which guarantees a steady development. Furthermore, this paper construct the chaos control to IS–LM fractional-order macroeconomic model by means of linear feedback control method, by calculating and adjusting the feedback coefficient, we make the system return to the convergence state.

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.

This paper studies a continuous Bertrand duopoly game model with two-stage delay. Our aim is to investigate the influence of delay and weight on the complex dynamic characteristics of the system. We obtain the bifurcation point of the system respect to delay parameter by calculating. In addition, the dynamic properties of the system are simulated by power spectrum, attractor, bifurcation diagram, the largest Lyapunov exponent, 3D surface chart, 4D Cubic Chart, 2D parameter bifurcation diagram, and 3D parameter bifurcation diagram. The results show that the stability of the system depends on the delay and weight, in order to maintain stability of price and ensure the firm profit, the firms must control the parameters in the reasonable region. Otherwise, the system will lose stability, and even into chaos, which will cause fluctuations in prices, the firms cannot be profitable. Finally, the chaos control of the system is carried out by a control strategy of the state variables’ feedback and parameter variation, which effectively avoid the damage of chaos to the economic system. Therefore, the results of this study have an important practical significance to make decisions with multi-stage delay for oligopoly firms.

According to a triopoly game model in the electricity market with bounded rational players, a new Cournot duopoly game model with delayed bounded rationality is established. The model is closer to the reality of the electricity market and worth spreading in oligopoly. By using the theory of bifurcations of dynamical systems, local stable region of Nash equilibrium point is obtained. Its complex dynamics is demonstrated by means of the largest Lyapunov exponent, bifurcation diagrams, phase portraits, and fractal dimensions. Since the output adjustment speed parameters are varied, the stability of Nash equilibrium gives rise to complex dynamics such as cycles of higher order and chaos. Furthermore, by using the straight-line stabilization method, the chaos can be eliminated. This paper has an important theoretical and practical significance to the electricity market under the background of developing new energy.

A dynamic triopoly game characterized by firms with different expectations is modeled by three-dimensional nonlinear difference equations, where the market has quadratic inverse demand function and the firm possesses cubic total cost function. The local stability of Nash equilibrium is studied. Numerical simulations are presented to show that the triopoly game model behaves chaotically with the variation of the parameters. We obtain the fractal dimension of the strange attractor, bifurcation diagrams, and Lyapunov exponents of the system.

A discrete-time financial system is proposed by using forward Euler scheme. Based on explicit Neimark-Sacker bifurcation (also called Hopf bifurcation for map) criterion, normal form method and center manifold theory, the system's existence, stability and direction of Neimark-Sacker bifurcation are studied. Numerical simulations are employed to validate the main results of this work. Some comparison of bifurcation between the discrete-time financial system and its continuous-time system is given.

This study attempts to characterize and predict stock returns series in Shanghai stock exchange using the concepts of nonlinear dynamical theory. Surrogate data method of multivariate time series shows that all the stock returns time series exhibit nonlinearity. Multivariate nonlinear prediction methods and univariate nonlinear prediction method, all of which use the concept of phase space reconstruction, are considered. The results indicate that multivariate nonlinear prediction model outperforms univariate nonlinear prediction model, local linear prediction method of multivariate time series outperforms local polynomial prediction method, and BP neural network method. Multivariate nonlinear prediction model is a useful tool for stock price prediction in emerging markets.

The paper presents a nonlinear discrete game model for two oligopolistic firms whose products are adnascent. (In biology, the term adnascent has only one sense, “growing to or on something else,” e.g., “moss is an adnascent plant.” See Webster's Revised Unabridged Dictionary published in 1913 by C. & G. Merriam Co., edited by Noah Porter.) The bifurcation of its Nash equilibrium is analyzed with Schwarzian derivative and normal form theory. Its complex dynamics is demonstrated by means of the largest Lyapunov exponents, fractal dimensions, bifurcation diagrams, and phase portraits. At last, bifurcation and chaos anticontrol of this system are studied.

Based on the work of domestic and foreign scholars and the application of chaotic systems theory, this paper presents an investigation simulation of retailer's demand and stock. In simulation of the interaction, the behavior of the system exhibits deterministic chaos with consideration of system constraints. By the method of space's reconstruction, the maximal Lyapunov exponent of retailer's demand model was calculated. The result shows the model is chaotic. By the results of bifurcation diagram of model parameters 𝑘, 𝑟 and changing initial condition, the system can be led to chaos.

We establish a nonlinear real estate model based on cobweb theory, where the demand function and supply function are quadratic. The stability conditions of the equilibrium are discussed. We demonstrate that as some parameters varied, the stability of Nash equilibrium is lost through period-doubling bifurcation. The chaotic features are justified numerically via computing maximal Lyapunov exponents and sensitive dependence on initial conditions. The delayed feedback control (DFC) method is applied to control the chaos of system.