A model for the problem of the cooperation/competition between infinite continuous species

In this paper we consider a particular type of differential equation that we can consider as a simple model for the problem of the cooperation/competition of infinite species. In this model each of the species meets each of the other species with a degree of competition or cooperation and their arrangements affect the evolution of the species. A first result of the existence of a unique, local-in-time, solution is given.     

Stability and Hopf bifurcation for a competition and cooperation model of two enterprises with delay

In this paper, a retarded competition and cooperation model of two enterprises is investigated. We first prove that the existence of the unique positive equilibrium for the mentioned model. By choosing the delay $\tau$ as a bifurcation parameter, we show that Hopf bifurcation at the positive equilibrium of the system can occur as $\tau$ crosses some critical values. Further, using the normal form theory and center manifold theorem, we derive the explicit algorithm determining the direction of Hopf bifurcations and the stability of the bifurcating periodic solutions. Finally, some numerical simulations supporting our theoretical results and the economic meaning of model are also included.     

A time-fractional competition ecological model with cross-diffusion

This paper is concerned with some mathematical and numerical aspects of a Lotka-Volterra competition time-fractional reaction-diffusion system with cross-diffusion effects. First, we study the existence of weak solutions of the model following the well-known Faedo-Galerkin approximation method and convergence arguments. We demonstrate the convergence of approximate solutions to actual solutions using the energy estimates. Next, the Galerkin finite element scheme is proposed for the considered model. Further, various numerical simulations are performed to show that the fractional-order derivative plays a significant role on the morphological changes of the considered competition model.     

A discrete cost sharing model with technological cooperation

This article proposes a setting that allows for technological cooperation in the cost sharing model. Dealing with discrete demands, we study two properties: additivity and dummy. We show that these properties are insufficient to guarantee a unit-flow representation similar to that of Wang (Econ Lett 64:187–192, 1999). To obtain a characterization of unit flows, we strengthen the dummy axiom and introduce a property that requires the cost share of every agent to be non-decreasing in the incremental costs generated by their demand. Finally, a fairness requirement as to the compensation of technological cooperation is examined.     

A Kolmogorov-type competition model with multiple coexistence states and its applications to plant competition for sunlight

It is demonstrated that a Kolmogorov-type competition model featuring species allocation and gain functions can possess multiple coexistence states. Two examples are constructed: one in which the two competing species possess rectangular allocation functions but distinct gain functions, and the other in which one species has a rectangular allocation function, the second species has a bi-rectangular allocation function, and the two species share a common gain function. In both examples, it is shown that the species nullclines may intersect multiple times within the interior of the first quadrant, thus creating both locally stable and unstable equilibrium points. These results have important applications in the study of plant competition for sunlight, in which the allocation functions describe the vertical placement of leaves for two competing species, and the gain functions represent rates of photosynthesis performed by leaves at different heights when shaded by overlying leaves belonging to either species.     

A diffusive competition model with a protection zone

This paper is concerned with a two species diffusive competition model with a protection zone for the weak competitor. Our mathematical results imply that when the protection zone is above a certain critical patch size determined by the birth rate of the weak competitor, the weak species almost always survives, but it cannot survive when the protection zone is below the critical size and its competitor is strong enough. While this is the main feature of the model, the actual dynamical behavior of the reaction-diffusion system is more complicated. The key to reveal the main feature of the system lies in a detailed analysis of the attracting regions of its steady-state solutions. Our mathematical analysis shows that, compared with the predator-prey model discussed in [Yihong Du, Junping Shi, A diffusive predator-prey model with a protect zone, J. Differential Equations 226 (2006) 63-91], the protection zone has some essentially different effects on the fine dynamics of the competition model.     

带有限反馈下层的二层规划问题的部分合作模型

对下层最优反馈为离散有限多个的二层规划问题的部分合作模型进行探讨. 当下层的合作程度依赖于上层的决策变量时, 给出一个确定合作系数函数的一般方法, 进而得到一个新的部分合作模型. 在适当地假设下, 可保证所给的部分合作模型一定可以找到比悲观解要好的解, 并结合新的部分合作模型对原不适定问题进行分析, 得到了一些有益的结论. 最后以实际算例说明了所给部分合作模型的可行性.     

Stochastic equations for two-type continuous-state branching processes with immigration and competition

A class of two-type continuous-state branching processes with immigration and competition is constructed as the solution of a jump-type stochastic integral equation system. We first show that the stochastic equation system has a pathwise unique non-negative strong solution and then prove the comparison property of the solution.     

A system-theoretic model for cooperation, interaction and allocation

A system-theoretic approach to cooperation, interaction and allocation is presented that simplifies, unifies and extends the results on classical cooperative games and their generalizations. In particular, a general Weber theory of linear values is obtained and a new theory for local cooperation and general interaction indices is established. The model is dynamic and based on the notion of states of cooperation that change under actions of agents. Careful distinction between “local” states of cooperation and general “system” states leads to a notion of entropy for arbitrary non-negative and efficient allocations and thus to a new information-theoretic criterion for fairness of allocation mechanisms. Shapley allocations, for instance, are exhibited as arising from random walks with maximal entropy. For a large class of cooperation systems, a characterization of game symmetries in terms of λ-values is given. A concept for cores and Weber sets is proposed and it is shown that a Weber set of a game with selection structure always contains the core.     

A supply chain network economic model with time-based competition

This paper presents an integrated model for time-cost competition between supply chains with heterogeneous customers. The firms in our model can offer various time options for their production/service to time-sensitive customers. This gives rise of a new concept of time-based supply chain, which we call T-chain, to be the basic element in the competition and extends the inter supply chain competition to a new dimension of time. Assuming the customers are heterogeneous in time-cost bi-criteria decision making, we integrate the discrete choice theory into supply chain network competition and formulate the equilibrium conditions as a multinomial logit based variational inequality problem. Numerical examples are presented for model illustration and managerial insights such as profit maximization for a firm who participates in this supply chain network.     

A predator-prey model with combined death and competition terms

The existence of a positive solution for the generalized predator-prey model for two species

A duopolistic spatial competition model with non-zero conjectural variation

Consider a two-stage non-cooperative Cournot game with location choice involving two firms. There aren spatially separated markets located at the vertices of a network. Each firm, first selects the location of a facility and then selects the quantities to supply to the markets in order to maximize its profit. Non-zero conjectural variation at the second stage is studied. Equilibrium in the quantities offered by each firm in the markets exists. Furthermore, when the demand in each market is sufficiently large, each firm chooses to locate its facility at the vertices. Partially financed by FEDER and Ministerio de Ciencia y Tecnología, grant BFM2002-04525-C02-01, and Universidad de Las Palmas de Gran Canaria, grant UNI2004/12     

A competition model for two resources in un-stirred chemostat

This paper studies a un-stirred chemostat with two species competing for two growth-limiting, non-reproducing resources. We determine the conditions for positive steady states of the two species, and then consider the global attractors of the model. In addition, we obtain the conditions under which the two populations uniformly strongly persist or go to extinction. Since the diffusion mechanism with homogeneous boundary conditions inhibits the growth of the organism species, it can be understood that the coexistence will be ensured by proportionally smaller diffusions for the two species. In particular, it is found that both instability and bi-stability subcases of the two semitrivial steady states are included in the coexistence region. The two populations will go to extinction when both possess large diffusion rates. If just one of them spreads faster with the other one diffusing slower, then the related semitrivial steady state will be globally attracting. The techniques used for the above results consist of the degree theory, the semigroup theory, and the maximum principle.     

A mathematical model of market competition

We consider a mathematical model of decision making by a company attempting to win a market share. We assume that the company releases its products to the market under the competitive conditions that another company is making similar products. Both companies can vary the kinds of their products on the market as well as the prices in accordance with consumer preferences. Each company aims to maximize its profit. A mathematical statement of the decision-making problem for the market players is a bilevel mathematical programming problem that reduces to a competitive facility location problem. As regards the latter, we propose a method for finding an upper bound for the optimal value of the objective function and an algorithm for constructing an approximate solution. The algorithm amounts to local ascent search in a neighborhood of a particular form, which starts with an initial approximate solution obtained simultaneously with an upper bound. We give a computational example of the problem under study which demonstrates the output of the algorithm.     

A model of far-sighted electoral competition

A model is described in which candidates adopt positions in sequences of election contests against opponents randomly drawn from a large population. Symmetric steady-state equilibria of the model require rational selection of positions by all candidates against the aggregated behavior of the population, taking into account constraints which an individual's current selections impose on his future selections.     

A dynamical model of electoral competition

The paper presents the specific framework and a set of simulations computed on the basis of a kinetic model of interest in the field of the Social Sciences. The model is a reduced version of a comprehensive more general one, and it relates to the specific case of a competing bipartisan political system. The model structure contains terms with localized interactions and mean field terms. In the first part of the paper the mathematical details of the model are recalled. In the second part the simulations are presented with reference to the various scenarios examined. Finally a discussion on research perspectives is formulated.     

A partial cooperation model for non-unique linear two-level decision problems

This paper examines a linear static Stackelberg game where the follower's optimal reaction is not unique. Traditionally, the problem has been approached using either an optimistic or a pessimistic framework, respectively, representing the two extreme situations of full cooperation and zero cooperation from the follower. However, partial cooperation from the follower is a viable option. For partial cooperation, the leader's optimal strategy may be neither optimistic nor pessimistic. Introducing a cooperation index to describe the degree of follower cooperation, we first formulate a partial cooperation model for the leader. The two-level problem is then reformulated into a single-level model. It is shown that the optimistic and pessimistic situations are special cases of the general model, and that the leader's optimal choice may be an intermediate solution.     

A coupled Maxwell integrodifferential model for magnetization processes

A mathematical model for instationary magnetization processes is considered, where the underlying spatial domain includes electrically conducting and nonconducting regions. The model accounts for the magnetic induction law that couples the given electrical voltage with the induced electrical current in the induction coil. By a theorem of Showalter on degenerate parabolic equations, theorems on existence, uniqueness, and regularity of the solution to the associated Maxwell integrodifferential system are proved.