QUALITATIVE ANALYSIS OF A DICRETE POPULATION MODEL

In this paper, authors study the qualitative behavior of solutions of the discrete population model xn-xn-1=xn (a+bxn-k-cx2n-k),where a ∈ (0, 1), b ∈ (-∞, 0),c ∈ (0,∞ ), and k is a positive integer. They hot only obtain necessary as well as sufficient and necessary conditions for the oscillation of ail eventually positive solutions about the positive equilibrium, but also obtain some sufficient conditions for the convergence of eventually positive solutions. Furthermore, authors also show that such model is uniformly persistent, and that all its eventually positive solutions are bounded.

Fluorometric Discrimination Technique of Phytoplankton Population Based on Wavelet Analysis

The discrete excitation-emission-matrix fluorescence spectra (EEMS) at 12 excitation wavelengths (400, 430, 450, 460, 470, 490, 500, 510, 525, 550, 570, and 590 nm) and emission wavelengths ranging from 600-750 nm were determined for 43 phytoplankton species. A two-rank fluorescence spectra database was established by wavelet analysis and a fluorometric discrimination technique for determining phytoplankton population was developed. For laboratory simulatively mixed samples, the samples mixed from 43 algal species (the algae of one division accounted for 25%, 50%, 75%, 85%, and 100% of the gross biomass, respectively), the average discrimination rates at the level of division were 65.0%, 87.5%, 98.6%, 99.0%, and 99.1%, with average relative contents of 18.9%, 44.5%, 68.9%, 73.4%, and 82.9%, respectively; the samples mixed from 32 red tide algal species (the dominant species accounted for 60%, 70%, 80%, 90%, and 100% of the gross biomass, respectively), the average correct discrimination rates of the dominant species at the level of genus were 63.3%, 74.2%, 78.8%, 83.4%, and 79.4%, respectively. For the 81 laboratory mixed samples with the dominant species accounting for 75% of the gross biomass (chlorophyll), the discrimination rates of the dominant species were 95.1% and 72.8% at the level of division and genus, respectively. For the 12 samples collected from the mesocosm experiment in Maidao Bay of Qingdao in August 2007, the dominant species of the 11 samples were recognized at the division level and the dominant species of four of the five samples in which the dominant species accounted for more than 80% of the gross biomass were discriminated at the genus level; for the 12 samples obtained from Jiaozhou Bay in August 2007, the dominant species of all the 12 samples were recognized at the division level. The technique can be directly applied to fluorescence spectrophotometers and to the developing of an in situ algae fluorescence auto-analyzer for phytoplankton population.