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A MATHEMATICAL PROGRAMMING MODEL FOR THE COEXISTENCE OF COMPETITIONS AND COOPERATIONS PROBLEMS

We study in this paper a mathematical programming model for the coexistence of competitions and cooperations problems. We introduce a new solution concept, s-optimal solution for the problem, which always exists under compact and continuous conditions. It is shown that an s-optimal solution can be obtained by solving a nonlinear programming problem. Some examples are given to explain how to compute an s-optimal solution.

Bifurcation control of a fractional-order delayed competition and cooperation model of two enterprises

The competition and cooperation among enterprises has become a hot topic and focus issue in today’s world. How to manage the enterprise well so as to achieve the maximum output is an important problem for enterprise managers. Optimizing output of two enterprises plays a key role in operating enterprises. Many scholars pay much attention to this aspect. However, the reports on the stability and Hopf bifurcation for fractional-order delayed competition and cooperation model of two enterprises are very few. This paper is concerned with the stability, the existence of Hopf bifurcation and the bifurcation control issue of fractionalorder delayed competition and cooperation model of two enterprises. Firstly, some new sufficient conditions that guarantee the stability and the existence of Hopf bifurcation for fractional-order delayed competition and cooperation model of two enterprises are obtained by regarding the delay as bifurcation parameter. Then a suitable time delayed feedback controller is designed to control the Hopf bifurcation for involved model. The study shows that the delay and the fractional order have an important effect on the stability and Hopf bifurcation of involved model. Some simulations justifying the validity of the derived analytical results are given. At last, we end this paper with a concise conclusion. The obtained results of this article are innovative and are of great significance in handling the competition and cooperation among enterprises.

Competitive and Cooperative-Based Strength Pareto Evolutionary Algorithm for Green Distributed Heterogeneous Flow Shop Scheduling

This work aims to resolve the distributed heterogeneous permutation flow shop scheduling problem(DHPFSP)with minimizing makespan and total energy consumption(TEC).To solve this NP-hard problem,this work proposed a competitive and cooperative-based strength Pareto evolutionary algorithm(CCSPEA)which contains the following features:1)An initialization based on three heuristic rules is developed to generate a population with great diversity and convergence.2)A comprehensive metric combining convergence and diversity metrics is used to better represent the heuristic information of a solution.3)A competitive selection is designed which divides the population into a winner and a loser swarms based on the comprehensive metric.4)A cooperative evolutionary schema is proposed for winner and loser swarms to accelerate the convergence of global search.5)Five local search strategies based on problem knowledge are designed to improve convergence.6)Aproblem-based energy-saving strategy is presented to reduce TEC.Finally,to evaluate the performance of CCSPEA,it is compared to four state-of-art and run on 22 instances based on the Taillard benchmark.The numerical experiment results demonstrate that 1)the proposed comprehensive metric can efficiently represent the heuristic information of each solution to help the later step divide the population.2)The global search based on the competitive and cooperative schema can accelerate loser solutions convergence and further improve the winner’s exploration.3)The problembased initialization,local search,and energy-saving strategies can efficiently reduce the makespan and TEC.4)The proposed CCSPEA is superior to the state-of-art for solving DHPFSP.

A MODIFIED TWO-DIMENSIONAL LOTKA-VOLTERRA MODEL WITH EXCHANGE BETWEEN COOPERATION AND COMPETITION

Under the assumptions that there exists exchange between cooperation and competition in some ecological systems, the paper provides a modei based on the Lotka-Volterra equations to describe the exchange in a two-dimensional system. Then dynamics of the model is studied in detail, the division of distinct regions associated with difFerent dynamics in the parameter space is obtained, and the biological significance of these dynamical properties represent is discussed.

Target Path Tracking Method of Intelligent Vehicle Based on Competitive Cooperative Game

To improve intelligent vehicle drive performance and avoid vehicle side-slip during target path tracking,a linearized four-wheel vehicle model is adopted as a predictive control model,and an intelligent ve-hicle target path tracking method based on a competitive cooperative game is proposed.The design variables are divided into different strategic spaces owned by each player by calculating the affecting factors of the design variables with objective functions and fuzzy clustering.Based on the competitive cooperative game model,each game player takes its payoff as a mono-objective to optimize its own strategic space and obtain the best strategy to deal with others.The best strategies were combined into the game strategy set.Considering the front wheel angle and side slip angle increment constraint,tire side-slip angle,and tire side slip deflection dynamics,it took the path tracking state model was used as the objective,function and the calculation was validated by competitive cooperative game theory.The results demonstrated the effectiveness of the proposed algorithm.The experimental results show that this method can track an intelligent vehicle quickly and steadily and has good real-time per-formance.

The Architecture and Trend of Competitive Cooperation between Two Major Powers in Asia-Pacific and China’s Diplomacy

The rise of China and the strategic readjustments of the United States catalyzes major changes with four new features for the Asia-Pacific geo-space. A, the Asia-Pacific geo-economic map witnesses a double competitive pattern. B, geo-security space shows a Sino-U.S. competitive and low-cooperative trend. C, geopolitical environment highlights the development model competition. D, the high-tech becomes the new driving force for the Asia-Pacific geo-environment changes. The domestic and overseas concerns with the status and prospects of the Asia-Pacific geo-environment focus on a debates between a resistant and confrontational architecture and a competitive cooperation trend. The author believes that the conditions for the resistant and confrontational pattern are no longer in existence and the regional pattern should be promoted in a direction of competitive cooperation.

Consensus of Second-Order Multi-Agent Systems with Time-Varying Delays and Antagonistic Interactions

This study investigates the consensus problem of second-order multi-agent systems subject to time- varying interval-like delays. The notion of consensus is extended to networks containing antagonistic interactions modeled by negative weights on the communication graph. A unified framework is established to address both the stationary and dynamic consensus issues in sampled-data settings. Using the reciprocally convex approach, a sufficient condition for consensus is derived in terms of matrix inequalities. Numerical examples are provided to illustrate the effectiveness of the proposed result.

Small into Isomorphisms on L_∞ Spaces

If T is an isomorphism of L∞（A,μ）into L∞（B,v）which satisfies the condition ||T|| ||T-1||≤1+ε,where（A,μ）is a σ-finite measure space then T/||T||is close to an isometry with an error less than 4ε1.

Qualitative Analysis of a Class of Competitive and Cooperative Systems

Hirsch[1,2] studied the limiting behavior of solutions of competitive or cooperative systems, and showed that ifL is an ω-limit set of a three-dimensional cooperative system, which contains no equilibrium, thenL is a nonattracting closed orbit. Smith[3] considered a three-dimensional irreducible competitive system and showed that an ω-limit set containing no equilibrium must be a closed orbit which has a simple Floquet multiplier λ<1, and may be attracting. In this paper we carry out the qualitative analysis of a class of competitive and cooperative systems, and a generalization of the result of Levine[4] is given. The stability problem of closed orbits raised in [5] and [6] is resolved.