Bloom dynamics under the effects of periodic driving forces

Phytoplankton bloom received considerable attention for many decades. Different approaches have been used to explain the bloom phenomena. In this paper, we study a Nutrient–Phytoplankton–Zooplankton (NPZ) model consisting of a periodic driving force in the growth rate of phytoplankton due to solar radiation and analyse the dynamics of the corresponding autonomous and non-autonomous systems in different parametric regions. Then we introduce a novel aspect to extend the model by incorporating another periodic driving force into the growth term of the phytoplankton due to sea surface temperature (SST), a key point of innovation. Temperature dependency of the maximum growth rate (${\mu }_{max}$) of the phytoplankton is modelled by the well-known $Q_{10}$ formulation: ${\mu }_{max}={\mu }_0\ast {\left(Q_{10}\right)}^{T/10}$, where ${\mu }_0$ is maximum growth at $0^o$C. Stability conditions for all three equilibrium points are expressed in terms of the new parameter ${\rho }_2$, which appears due to the incorporation of periodic driving forces. System dynamics is explored through a detailed bifurcation analysis, both mathematically and numerically, with respect to the light and temperature dependent phytoplankton growth response. Bloom phenomenon is explained by the saddle point bloom mechanism even when the co-existing equilibrium point does not exist for some values of ${\rho }_2$. Solar radiation and SST are modelled using sinusoidal functions constructed from satellite data. Our results of the proposed model describe the initiation of the phytoplankton bloom better than an existing model for the region 25–35° W, 40–45° N of the North Atlantic Ocean. An improvement of 14 days (approximately) is observed in the bloom initiation time. The rate of change method (ROC) is applied to predict the bloom initiation.