CATASTROPHE THEORY APPLIED TO WATER QUALITY REGULATION OF RIVERS

Abstract From experimental data over a year, the oxygen concentration in rivers water versus the temperature exhibits a hysteresis cycle. It means that, at each temperature, two different values of oxygen concentration exist. This paper deals with a mathematical model of the annual dynamics of oxygen concentration in rivers water in taking into account (i) the exchange of oxygen between air and water, (ii) the production of oxygen by photosynthesis and (iii) the consumption of oxygen by respiration. The behavior surface of the oxygen concentration corresponds to a cusp in the framework of catastrophe theory. For critical values of the control parameters (temperatures, nutrients), one assists to a sharp growth or decay of the oxygen concentration in water.