The time delays influence on the dynamical complexity of algal blooms in the presence of bacteria

Bacteria associated with oceanic algal blooms are acknowledged to play important roles in carbon, nitrogen, and sulfur cycling. They influence the climate, mediate primary production, participate in biogeochemical cycles, and maintain ecological balance. A greater insight on the control of the interactions between microalgae and other microorganisms, particularly bacteria, would be helpful in exploring the role of bacteria on algal blooms in lakes. The present study is to investigate the effects of bacteria on the occurrence of algal blooms in lakes. We propose a nonlinear mathematical model by taking into account interactions among nutrients, algae, detritus and bacteria in a lake. We assume that bacteria enhance the growth of algal biomass through remineralization only. Equilibria are analyzed for feasibility and stability, substantiated via numerical simulations. Increase in uptake rate of nutrients by algae and bacteria death rate generates transcritical bifurcations. We perform a global sensitivity analysis to identify the important parameters of the model having a significant impact on the densities of algae and bacteria in the lake. Our findings show that massive algal production might occur in the presence of bacteria, and microalgae-bacteria interactions can be beneficial to the massive production of microalgae. Further, the effect of time delays involved in the bacterial decomposition conversion of detritus into nutrients is studied. Chaotic oscillations may arise via equilibrium destabilization on increasing the values of the time lag. To support chaos occurrence, the Poincaré map is drawn and the Lyapunov exponents are also computed. The findings, critically important for lake restoration, indicate that hypoxia in the lake can be prevented if detritus removal is performed on a regular basis, at time intervals smaller than the critical threshold in the delay with which detritus is decomposed into nutrients.