Studies On Non-linear Dynamics Of Macroscopic And Microscopic Ecosystem And Mechanism Of Filamentous Bulking

The model of three-species food chain is firstly studied in the paper. Throughcomparative analyses on the models with time delay effect (TDE) and without TDE,we find the model without TDE converges finally to a stable equilibrium point. Whilethe model with TDE will go through Hopf bifurcation and period-doubling bifurcationwith the increase of TDE, eventually move towards the chaos. Route to chaos throughperiod-doubling by TDE seems to hold Feigenbaum's number-alike universality.Furthermore, the origin of a variety of states of stability, periodic fluctuation,multi-periodic fluctuation, chaos and extinction are unified in a new perspective ofTDE. It is a logical conclusion that TDE may play a vital role in producingcomplexity of ecosystems.All biology in macroscopic and microscopic ecosystem follow the unified growthlaw, thus it should logically be described as the uniform model. But there currentlyexists different models in macroscopic and microscopic fields. Based on theirpreferences and characteristics the author investigates the distinction between twomodels. Besides, Monod equation as an empirical equation describing themicroorganism growth is not available for the solution with the high microorganismconcentration and the low substrate concentration. So the substrate-revised Monodequation(SRME) is proposed, which can better describe the microorganism growth ina generic way.In the end, on the basis of SRME, a prototype mathematical model is proposed todescribe the interactions among filamentous, floc-forming bacteria and protozoanwithin the completely mixed activated sludge systems. In view of its greatfluctuation-resisting capacity, substrate concentration is assumed as a stable parameterfor convenience of analysis. In this case, the long-term behaviors of the threemicro-organisms at different substrate concentrations and for varying dilution ratesare analyzed. Base on the above analysis, the possibility of occurrence of filamentousbulking for different operating conditions is investigated in the practical system withsubstrate fluctuation. The results show the model is capable of describing the practicalcoexistence of the three micro-organisms in a generic way, and filamentous bulkingwill occur within a studied range of substrate concentration under unsuitable dilutionrate, particularly at low substrate concentration. When substrate concentrationfluctuates, the synchronous control parameter is helpful to prevent filamentousbulking. Thus, the paper reveals the cause of filamentous bulking theoretically, andmay provide crucial theoretical foundation for the settlement of filamentous bulking.