Matter growth in extended ΛCDM cosmology

On the basis of a previously established scalar–tensor extension of the [Formula: see text]CDM model, we develop an effective fluid approach for the matter growth function. This extended [Formula: see text]CDM (henceforth [Formula: see text]CDM) cosmology takes into account deviations from the Standard Model both via a modified background expansion and by the inclusion of geometric anisotropic stresses as well as of perturbations of the geometric dark-energy equivalent. The background dynamics is governed by an explicit analytic expression for the Hubble rate in which modifications of the Standard Model are given in terms of a single constant parameter [W. C. Algoner, H. E. S. Velten and W. Zimdahl, J. Cosmol. Astropart. Phys. 1611 (2016) 034]. To close the system of fluid-dynamical perturbation equations, we introduce two phenomenological parameters through which the anisotropic stress is related both to the total energy density perturbation of the cosmic substratum and to relative perturbations in the effective two-component system. We quantify the impact of deviations from the standard background, of anisotropic stresses and of nonvanishing perturbations of the effective dark-energy component on the matter growth rate function [Formula: see text] and confront the results with recent redshift-space distortion (RSD) measurements.

Tragedy of the Commons in the Chemostat

We present a proof of principle for the phenomenon of the tragedy of the commons that is at the center of many theories on the evolution of cooperation. We establish the tragedy in the context of a general chemostat model with two species, the cooperator and the cheater. Both species have the same growth rate function and yield constant, but the cooperator allocates a portion of the nutrient uptake towards the production of a public good -the “Commons” in the Tragedy-which is needed to digest the externally supplied nutrient. The cheater on the other hand does not produce this enzyme, and allocates all nutrient uptake towards its own growth. We prove that when the cheater is present initially, both the cooperator and the cheater will eventually go extinct, hereby confirming the occurrence of the tragedy. We also show that without the cheater, the cooperator can survive indefinitely, provided that at least a low level of public good or processed nutrient is available initially. Our results provide a predictive framework for the analysis of cooperator-cheater dynamics in a powerful model system of experimental evolution.

Disturbance Attenuation via Output Feedback for Uncertain Nonlinear Systems with Output and Input Depending Growth Rate

The problem of output feedback disturbance attenuation is investigated for a class of uncertain nonlinear systems. The uncertainties of the considered systems are bounded by unmeasured states with growth rate function of output and input multiplying an unknown constant. Based on a dynamic gain observer, an adaptive output feedback controller is proposed such that the states of the closed-loop system are globally bounded, and the disturbance attenuation is achieved in theL2-gain sense. An example is provided to demonstrate the effectiveness of the proposed design scheme.

Optimal Periodic Harvesting Strategy for the General Autonomous System of Single Specie

We study a optimal control problem-optimal periodic harvesting strategy for the general autonomous system of single specie. Suppose the growth rate function f(x) is C^2, x* satisfies f'(x*)=0. We proved that if f"(x*)<0，then x* is the optimal trajectory, otherwise, x* is not the optimal trajectory.

Logistic equation with thep-Laplacian and constant yield harvesting

We consider the positive solutions of a quasilinear elliptic equation withp-Laplacian, logistic-type growth rate function, and a constant yield harvesting. We use sub-super-solution methods to prove the existence of a maximal positive solution when the harvesting rate is under a certain positive constant.