Bifurcations of optimal vector fields in the shallow lake model

The solution structure of the set of optimal solutions of the shallow lake problem, a problem of optimal pollution management, is studied as we vary the values of the system parameters: the natural resilience, the relative importance of the resource for social welfare and the future discount rate. We find parameter values at which qualitative changes occur. Using theoretical results on the bifurcations of the solution structure to infinite horizon optimization problems obtained earlier, we give a fairly complete bifurcation analysis of the shallow lake problem. In particular, we show how the increase of the discount rate affects the parameter regions where an oligotrophic steady state, corresponding to low pollution level, is globally stable or locally stable under optimal dynamics. Asymptotically, an increase of the discount rate can be offset with a proportional increase of the relative social weight of the resource.

Bifurcations of optimal vector fields in the shallow lake system

The shallow lake problem is a nonconvex production-pollution dynamic optimisation problem whose solution structure depends nonlinearly on the system parameters. We perform a bifurcation analysis to investigate the consequences of varying the relative cost of pollution and the discount rate.

Is more memory in evolutionary selection (de)stabilizing?

We investigate the effects of memory on the stability of evolutionary selection dynamics based on a multi-nomial logit model in an asset pricing model with heterogeneous beliefs. Whether memory is stabilizing or destabilizing depends in general on three key factors: (1) whether or not the weights on past observations are normalized; (2) the ecology of forecasting rules, in particular the average strength of trend extrapolation and the spread in biased forecasts, and (3) whether or not costs for information gathering of economic fundamentals have to be incurred.

The algebraic hyperstructure of elementary particles in physical theory

Algebraic hyperstructures represent a natural extension of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. Algebraic hyperstructure theory has a multiplicity of applications to other disciplines. The main purpose of this paper is to provide examples of hyperstructures associated with elementary particles in physical theory.Comment: 13 page

Increasing the Adaptive Capacity of the Organism When Exposed to Adverse Environmental Factors Through Phytoadaptogens

The Problem of improving the quality of life of the population in modern conditions is the most relevant. The level of human health largely depends on the quality of the environment. Of special importance are the risk factors for the spread of diseases like environmental pollution, social conditions and bad habits. To the emergence of ecologically dependent diseases leads the combined impact of technogenic, social-economic, natural-climatic factors. The introduction of the principles of biotechnology, nanotechnology and innovations in industrial processing of plant resources, especially natural adaptogens, contributes to the production of balanced, ecologically clean food products functional purpose, the use of which will significantly minimize the adverse effects of the environment on humans