Temperature dependent growth rate of phytoplankton and salinity induced grazing rate of zooplankton as determinants of realistic multi-delayed food chain model

Abstract

Impact of temperature dependent growth rate of phytoplankton, salinity induced grazing rate of zooplankton and gestation delay of phytoplankton and zooplankton differently are considered in the present study. Reproduction of predator after consuming prey is not instantaneous, but mediated by some time lag required for gestation. Here first gestation delay is considered in the numerical response term of phytoplankton and second one is at the numerical response term of zooplankton respectively. There is a very interesting interplay between these two delays. In accordance with previous studies, it is observed that delay destabilizes the system, in general and stability loss occurs via Hopf-bifurcation. In particular, we show that there exists critical values of the delay parameters below which the coexistence equilibrium is stable and above which it is unstable. Hopf bifurcation occurs when the delay parameters cross their critical values. All the stability results of the system significantly depend upon the temperature and salinity of the environment. Numerical examples are also support the model assumption and analytical results.

Evolution of primary production and its drivers on the Lebanese coast between 1986 and 2013

“…Models offer a way to synthesize our understanding of the environment, analyse changes in ecosystems, and forecast future changes (Fadel et al 2019;Jickells et al 2015). Hydrodynamicecological models can help us to understand the dynamics and the controlling factors of primary production (Fadel et al 2017;Roy et al 2016;Sharip et al 2016;Vinçon-Leite et al 2017).…”