A mathematical study for chaotic dynamics of dissolved oxygen- phytoplankton interactions under environmental driving factors and time lag

Dynamics of the species in the ecosystem is constantly influenced by environmental variations, e.g. salinity, nutrient and temperature are among commonly investigated factors by ecologists. The changes in the environmental factors are expected to have an impact on the rate of photosynthesis. The main objective of this study is to theoretically analyse the temporal and spatial changes in the oxygen and phytoplankton dynamics with time delay as response to varying oxygen production rate over the daily cycle. In order to analyse the effect of environmental driving forces, two forms of time dependent oxygen production rate are considered: (i) linear form and (ii) bell shape form that, in theory, mimics the peaks in the oxygen production in a daily cycle. The model equations are investigated with constant time delay in phytoplankton growth to transform the systems into a biologically more realistic form. In fact, the numerical and theoretical investigations of this paper show that, regardless of the parameter choice, the spatial and non-spatial versions of the model are not rewarded with complex dynamics in the absence of time delay and do not have a tendency to oscillate. It is confirmed that sufficiently large values of time delay not only induce chaotic oscillations at the onset of a travelling population front but also play a destabilising role, leading to oscillatory limit-cycle behaviour in the dynamics. The findings of this paper show that, when the time delay is incorporated in plankton growth terms, time dependent oxygen production rate through environmental variations may have a substantial impact on the persistence, extinction and stability of species in the ecosystem.