Optimal fishery with coastal catch

In many spatial resource models, it is assumed that an agent is able to harvest the resource over the complete spatial domain. However, agents frequently only have access to a resource at particular locations at which a moving biomass, such as fish or game, may be caught or hunted. Here, we analyze an infinite time‐horizon optimal control problem with boundary harvesting and (systems of) parabolic partial differential equations as state dynamics. We formally derive the associated canonical system, consisting of a forward–backward diffusion system with boundary controls, and numerically compute the canonical steady states and the optimal time‐dependent paths, and their dependence on parameters. We start with some one‐species fishing models, and then extend the analysis to a predator–prey model of the Lotka–Volterra type. The models are rather generic, and our methods are quite general, and thus should be applicable to large classes of structurally similar bioeconomic problems with boundary controls. Recommedations for Resource Managers Just like ordinary differential equation‐constrained (optimal) control problems and distributed partial differential equation (PDE) constrained control problems, boundary control problems with PDE state dynamics may be formally treated by the Pontryagin's maximum principle or canonical system formalism (state and adjoint PDEs). These problems may have multiple (locally) optimal solutions; a first overview of suitable choices can be obtained by identifying canonical steady states. The computation of canonical paths toward some optimal steady state yields temporal information about the optimal harvesting, possibly including waiting time behavior for the stock to recover from a low‐stock initial state, and nonmonotonic (in time) harvesting efforts. Multispecies fishery models may lead to asymmetric effects; for instance, it may be optimal to capture a predator species to protect the prey, even for high costs and low market values of the predators

Coexistence and optimal control problems for a degenerate predator-prey model

In this paper we present a predator-prey mathematical model for two biological populations which dislike crowding. The model consists of a system of two degenerate parabolic equations with nonlocal terms and drifts. We provide conditions on the system ensuring the periodic coexistence, namely the existence of two non-trivial non-negative periodic solutions representing the densities of the two populations. We assume that the predator species is harvested if its density exceeds a given threshold. A minimization problem for a cost functional associated with this process and with some other significant parameters of the model is also considered. \ua9 2010 Elsevier Inc

Optimizing high-dimensional stochastic forestry via reinforcement learning

In proceeding beyond the generic optimal rotation model, forest economic research has applied various specifications that aim to circumvent the problems of high dimensional-ity. We specify an age-and size-structured mixed-species optimal harvesting model with binary variables for harvest timing, stochastic stand growth, and stochastic prices. Rein-forcement learning allows solving this high-dimensional model without simplifications. In addition to presenting new features in reservation price schedules and effects of stochas-ticity, our setup allows evaluating the simplifications in the existing research. We find that one-or two-dimensional models lose a high fraction of attainable economic output while the commonly applied size-structured matrix model overestimates economic profitability, yields deviations in harvest timing, including optimal rotation, and dilutes the effects of stochasticity. Reinforcement learning is found to be an efficient and promising method for detailed age-and size-structured optimization models in resource economics. (c) 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )Peer reviewe

Extending Feynman's Formalisms for Modelling Human Joint Action Coordination

The recently developed Life-Space-Foam approach to goal-directed human action deals with individual actor dynamics. This paper applies the model to characterize the dynamics of co-action by two or more actors. This dynamics is modelled by: (i) a two-term joint action (including cognitive/motivatonal potential and kinetic energy), and (ii) its associated adaptive path integral, representing an infinite--dimensional neural network. Its feedback adaptation loop has been derived from Bernstein's concepts of sensory corrections loop in human motor control and Brooks' subsumption architectures in robotics. Potential applications of the proposed model in human--robot interaction research are discussed. Keywords: Psycho--physics, human joint action, path integralsComment: 6 pages, Late

The Premium of Marine Protected Areas: A Simple Valuation Model

The article addresses the induced cost, the premium, from establishing a marine protected area in a deterministic model of a fishery. Outside the protected area, the fishery is managed optimally through total allowable catch quotas. The premium is found to be increasing and convex along the protection parameter. Biological measures are introduced to increase the understanding of the mechanisms in the bioeconomic system. Time-series solutions show that the net return per unit of fish increases after the protected area is established.Bioeconomics, dynamic programming, fisheries management, marine protected areas, migration, modeling, optimization, renewable resources., International Development, International Relations/Trade, Political Economy, Research and Development/Tech Change/Emerging Technologies, C61, Q22, Q57.,

Kinetic Intersections as a Source of Information on Rate Coefficients

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Spatial Analysis: Development of Descriptive and Normative Methods with Applications to Economic-Ecological Modelling

This paper adapts Turing analysis and applies it to dynamic bioeconomic problems where the interaction of coupled economic and ecological dynamics over space endogenously creates (or destroys) spatial heterogeneity. It also extends Turing analysis to standard recursive optimal control frameworks in economic analysis and applies it to dynamic bioeconomic problems where the interaction of coupled economic and ecological dynamics under optimal control over space creates a challenge to analytical tractability. We show how an appropriate formulation of the problem reduces analysis to a tractable extension of linearization methods applied to the spatial analog of the well known costate/state dynamics. We illustrate the usefulness of our methods on bioeconomic applications, but the methods have more general economic applications where spatial considerations are important. We believe that the extension of Turing analysis and the theory associated with dispersion relationship to recursive infinite horizon optimal control settings is new.Spatial analysis, Economic-ecological modelling