Endogenous optimization fisheries models

This paper deals with a special class of fisheries models referred to as endogenous optimization models. The distinctive feature of these models is that behaviour of the agents in the model is not predetermined by exogenous behavioural rules. In endogenous optimization models, the model agents are merely furnished with objectives such as profit or utility maximization. Given these objectives and the various constraints determined by the state of the model at each point of time, the agents solve their maximization problem. The corresponding values of their control variables then constitute their behaviour.Having generated individual agents' behaviour by endogenous optimization, summing over agents yields aggregate behaviour. Aggregate behaviour must conform with the overall constraints of the model, be they physical or otherwise. Within the market system, individual behaviour or rather plans are made compatible via changes in relative prices. Therefore, outside equilibrium, behavioural plans must be repeatedly modified to become mutually compatible. This implies iteratively solving the maximization problem of a number of different agents. Endogenous optimization models therefore tend to be computationally very demanding.Clearly, the basic principles of endogenous optimization are just as applicable to any model involving maximizing agents.     

Qualitative analysis of an Ivlev-type bio-economic system

The paper considers a bio-economic system with Ivlev-type functional response. Formally, our bio-economic system takes the form of differential-algebraic equations. We investigate Hopf bifurcation and center stability of the proposed bio-economic system. Some easily verifiable criteria are obtained on these issues. Finally, a numerical example is supplied to illustrate the effectiveness of our criteria.     

About the entropic structure of detailed balanced multi-species cross-diffusion equations

This paper links at the formal level the entropy structure of a multi-species cross-diffusion system of Shigesada–Kawasaki–Teramoto (SKT) type (cf. [1]) satisfying the detailed balance condition with the entropy structure of a reversible microscopic many-particle Markov process on a discretised space. The link is established by first performing a mean-field limit to a master equation over discretised space. Then the spatial discretisation limit is performed in a completely rigorous way. This by itself provides a novel strategy for proving global existence of weak solutions to a class of cross-diffusion systems.     

Permanence and convergence in multi-species competition systems with delay

The permanence and global attractivity of positive equilibria are obtained for some multi-species Kolmogorov competition models with delay by embedding the system into a larger cooperative system with delay and then appealing to the theory of monotone dynamical systems.

     

Existence and nonexistence of positive steady states in multi-species phytoplankton dynamics

In this paper we study a nonlocal reaction–diffusion–advection system modeling the growth of multiple competitive phytoplankton species in a vertical water column with incomplete mixing. We find that when the diffusion of the system is large, there is no positive steady states, and when the diffusion is not large, there exists at least one positive steady states under certain conditions. The main tools we use are the fixed point index theory, a refined comparison theorem and fine properties of the principal eigenvalues.     

The management of high seas fisheries

The intergovernmental United Nations Conference on Highly Migratory and Straddling Stocks, initiated in 1993 and finished in 1995, addressed the conservation and management of fishery resources located both within the coastal state 200 mile Exclusive Economic Zone (EEZ) and the adjacent high seas. These types of marine resources continue to be a source for international conflicts and debates. The original United Nations Law of the Sea of 1982 failed to address transboundary fisheries in a proper way. In particular, the agreement did not recognize the emergence of the complicated straddling stock issue. In the new United Nations Law of the Sea agreement of 1995, a consensus was reached that the management of the straddling and highly migratory fish stocks should be carried out through regional fisheries management organizations. We present a review of the straddling stock issues in the international agreement emerging from the negotiations within the United Nations. The review is contrasted with and clarified by game theoretic analyses. We also discuss one international fishery exemplifying the case, the Norwegian springspawning herring. The main conclusion is that the local problems, faced during the stage of setting up regional fisheries organizations for the management of straddling and highly migratory fish stocks, are expected to be much more complicated and difficult to solve as compared to the cases of shared fish stocks. In the current paper, we present two reasons for this increased complexity. The first is the larger number of players as compared to the case of shared fish stocks and the second is the possibility of new members entering the regional fisheries organizations.     

超燃冲压发动机性能的准二维计算方法

为了能在双模态超燃冲压发动机流道方案初步论证中提供一种较快速的发动机性能计算方法,在二维N-S方程基础上,引入一维完全燃烧计算方法,提出了预估超燃冲压发动机性能的准二维计算方法。该方法能够计入激波、边界层分离等对发动机性能的影响,可在较短时间计算出整机推力、比冲性能和沿程热力学参数。通过对自由射流发动机计算,验证了此方法。并在此基础上,初步分析了燃料喷注位置和流道构型对发动机性能的影响。      

Stability analysis for a new model of multi-species convection-diffusion-reaction in poroelastic tissue

We perform the linear stability analysis of a new model for poromechanical processes with inertia (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes convected in the medium. We find parameter regions that lead to spatio-temporal instabilities of the coupled system. The mutual dependences between deformation and diffusive patterns are of substantial relevance in the study of morphoelastic changes in bio-materials. We provide a set of computational examples in 2D and 3D (related to brain mechanobiology) that can be used to form a better understanding on how, and up to which extent, the deformations of the porous structure dictate the generation and suppression of spatial patterning dynamics, also related to the onset of mechano-chemical waves.     

Start-up of multi-species anaerobic digestion systems: extrapolation of the single species approach

This paper presents a brief evaluation of a start-up strategy for multi-species anaerobic digestion systems modelled as two-step reaction systems, where acidogenesis is described by Monod kinetics while the methanogenesis is described by Haldane kinetics. The start-up policy has been developed originally for single species systems with the aim of maximizing the biogas outflow rate. It consists of switching the dilution rate from minimum to maximum and then to the optimal value (bang-bang control) in order to bring the system from an arbitrary initial condition to the optimal set-point. This start-up strategy is applied to the multi-species system using an averaged model, which is usually the only model that can be identified for a multi-species system, as measuring individual biomasses is almost impossible in practice. Even the development of an accurate averaged model, fully characterizing the system dynamics based on the variation of the species proportions is difficult. The averaged models used in this study are built based on a more or less accurate knowledge of the species proportions and their kinetics at the start-up instant and used as such in the application of the start-up policy. It is shown that the start-up policy leads to an efficient ecosystem, characterized by high outflow rate of biogas, which is very close to the maximum even in the case of an inaccurate averaged model. The influence of the model accuracy on the system stability and its productivity is discussed. This study can also be viewed as a robustness evaluation with respect to model inaccuracy of the single species start-up strategy, as the process changes from the averaged kinetics to the kinetics of the winning species during species selection.     

Individual-based modelling and simulation of microbial processes: yeast fermentation and multi-species composting

Controlled microbial activity is the core of many industrial processes. Such dynamic microbial processes must be carefully studied to optimize their application. They are usually tackled by means of continuous mathematical modelling at the population level (top-down). An alternative approach is individual-based modelling (IbM) (bottom-up). INDISIM is a discrete and spatially explicit IbM. It sets the rules that govern each microbe and its interaction with its local environment, as well as the significant environmental processes. Then it performs simulations that include a large number of microbes, and the behaviour of the whole system emerges. The rules are changed to reproduce the behaviour of microbes depending on the system to be studied. Two adaptations of INDISIM to study yeast fermentations and multi-species composting are presented in this article (INDISIM-YEAST and INDISIM-COMP), proof of INDISIM's versatility. A few representative results are also shown.     

Mid-term and short-term planning support for home health care services

In this paper we are looking at routing and scheduling problems arising in the context of home health care services. Many small companies are working in this sector in Germany and planning is still done manually, resulting in long planning times and relatively inflexible solutions.     

Dynamics of multi-species competition-predator system with impulsive perturbations and Holling type III functional responses

We investigate the dynamics of a class of multi-species predator-prey interaction models with Holling type III functional responses based on systems of nonautonomous differential equations with impulsive perturbations. Sufficient conditions for existence of a positive periodic solution are investigated by using a continuation theorem in coincidence degree theory, which have been extensively applied in studying existence problems in differential equations and difference equations. In addition, sufficient criteria are established for the global stability and the globally exponential stability of the system by using the comparison principle and the Lyapunov method.     

Layoff costs and underutilization of labour in fisheries

The cost of reducing the labour force during a transition from an overexploited fishery to a bionomic fishery is taken into account. This affects both the long run steady state and the optimal approach to steady state. These effects are illustrated using the case of the NortheastArctic cod stock as a stylized example. The method outlined represents an operational way to assess harvest quotas as well as effort quotas both in the steady state and not least on the path to steady state. In the steady state analysis completely general functional forms are used, whereas in the optimal path analysis the objective function is required to be quadratic in the control variable. This requirement, however, incorporates the most important sources of nonlinearities such as downward sloping demand and increasing marginal costs.     

Global weak solutions of a three-dimensional flow model for a multi-species mixture in porous media

We consider an initial boundary value problem for a non-linear differential system consisting of one equation of parabolic type coupled with a n × n semi-linear hyperbolic system of first order. This system of equations describes the compressible miscible displacement of n + 1 chemical species in a porous medium, in the absence of diffusion and dispersion. We assume the viscosity of the fluid mixture to be constant. We prove, in three space dimensions, the existence of a global weak solution with non-smooth initial data for the concentration. The proof is based on the artificial viscosity method together with a compensated compactness argument. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.     

Existence and exponential stability of almost periodic solutions for a neutral multi-species Logarithmic population model

In this paper, we study the almost periodic solution for a neutral multi-species Logarithmic population model. By employing Banach’s fixed point theorem and using differential inequality technique, we present some sufficient conditions ensuring the existence, uniqueness and globally exponential stability of almost periodic solution for the model. The results obtained extend and improve the earlier publications. Finally, two examples are provided to show the correctness of our analysis.     

Global solutions to a class of multi-species reaction-diffusion systems with cross-diffusions arising in population dynamics

In this paper, an n$n$-species strongly coupled cooperating diffusive system is considered in a bounded smooth domain, subject to homogeneous Neumann boundary conditions. Employing the method of energy estimates, we obtain some conditions on the diffusion matrix and inter-specific cooperatives to ensure the global existence and uniform boundedness of a nonnegative solution. The globally asymptotical stability of the constant positive steady state is also discussed. As a consequence, all the results hold true for multi-species Lotka–Volterra type competition model and prey–predator model.     

Modelling complex human systems: A fisheries example

The basis of current models used in Fishery Management is briefly examined, and various shortcomings are discussed. Alternative, dynamic models are described which are based on the data available for the Nova Scotia Groundfish Fisheries. It is shown that human responses can amplify relatively small annual environmental fluctuations, leading to large, quasi- cyclic changes in catch and profit. In a detailed spatial model it is shown that stochastic behaviour on the part of some fishermen is necessary for the survival of the fishery, and that the efficiency and size of the industry depends very much on the information flows concerning catch. A very general discussion is given which shows how these ideas are important in our understanding of innovation and discovery in general terms.     

A model of rational equilibrium in quota-regulated multiple-species fisheries

This paper derives rational ecological–economic equilibrium outcomes—capital and variable input allocations, harvests, discards, revenue, costs, and stock abundances—in a spatially heterogeneous, multispecies fishery that is regulated with individual fishing quotas (IFQs). The production setting is decentralized; a manager chooses species-specific, seasonal, and spatially nondelineated quotas. Industry controls all aspects of harvesting operations. We present a solution concept and computational algorithm to solve for equilibrium harvests, discards, and profits across species, space, and time (within the regulatory cycle). The rational equilibrium mapping that we derive, used recursively, can be used to implement management-preferred bioeconomic outcomes. The model offers an essential IFQ regulation-to-outcome mapping that enables more precise implementation of management goals in multiple-species and heterogeneous fishery settings. Recommendations for Resource Managers Knowing where and when individual tradeable fishing quotas will be utilized across heterogeneous space and time in multiple-species fisheries is essential for effective fisheries management. Ad hoc models, while simple, contribute to “implementation uncertainty” whereby predicted mortality, discards, cost, and rent outcomes across fish species, space, and time are poorly matched to the realized outcomes that are implemented by resource users. A model of rational equilibrium mortality, discards, costs, and rent across space and time offers and powerful tool to improve the management of quota-regulated fisheries.