Yields richer and considerably different system behaviour. In its most general form, the dynamics reads as: Therefore, different forms of predator–prey dynamics have been proposed. Additionally, a more refined representation of the ‘response’ of the predator population to prey supply could be substituted for bx( t) ≥ 0 and could thus include upper boundaries on consumption necessary per time unit, or whether or not ecological niches are occupied. For other prey species with, e.g., intraspecific competition, ax( t) ≥ 0 has to be replaced by a logistic growth function. Therefore, we can also use Goodwin’s economic interpretation for the two variables: in his model predator takes on the role of wage rate and prey takes on the role of employment rate.ĭue to the linear dependence on food, the basic Lotka–Volterra system ( 1) is suitable for prey species that do not experience any capacity constraints. Both products can be managed in optional quantities without any effect on market prices. We are assuming a restricted territory as a biotope or a forest, which obviously limits the population of prey.Īccording to Goodwin ( 19), we also can apply the setting to business cycles with variables x as an intermediate product and variable y as the final product, created by one input only. Variable y( t) represents a predator population (as predator fish) at time t with the prey as exclusive source of food. Variable x( t) represents a prey population (as prey fish) at time t that grows exponentially in the absence of predators. 4).įinally, we close with a summary where we have to admit that handling such a complex system can only give us some heuristic explanations with empirical evidence. With the help of an experimental setting in order to ascertain how successful human decision makers are in managing such a system we are able to demonstrate interesting results (Sect. Therefore, we create a decision support tool which should help us to understand human behaviour within complex systems in which the price of harvested objects plays an important role on one hand and the availability of the objects are important on the other side. Our aim consists mainly in collecting information how subjects handle such a complex system. 3 shows applications of predator–prey models for optimal harvesting and refers mainly to behavioural economics. In principle, our goal is to yield some findings in economic stabilisation, but, mainly for reasons of simplicity, the application at hand tackles the problem in the field of biology.Ī biotope consisting of two populations should be brought to a stationary fixpoint level by means of two different instruments. Therefore, we give some theoretical background of predator–prey type models including economic interpretations of those models in the following section. As a basis we use a well-known class of dynamical systems-predator–prey models-which is applied to a specific situation. We focus on a complex system and the question how to handle it. This aspect could become a new important aspect in economics in general and in sustainable environments especially. We have developed a most interesting simulation model, where it will turn out that prices play a less important role than availability of the goods. With the methodology of experimental economics, the experiment at hand is developed to analyse the capability of individual persons to handle a complex system, and to find an economic, stable equilibrium in a neutral setting. We find interesting insights from those who manage the dynamic system. We aim to analyse a sustainable environment with diametrical goals to harvest as much as possible while allowing optimal population growth. Our economic experiments are able to test the applicability of these strategies, and in how far decision-makers can learn to improve decision-making by repeated applications. We get new insights derived from experimental approaches: analytical models (optimal dynamic control of predator–prey models) provide optimal dynamic strategies and interventions, depending on different objective functions. This paper combines work to use a decision support tool for sustainable economic development, while acknowledging interdependent dynamics of population density, and interferences from outside.
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