Modeling the plankton–fish dynamics with top predator interference and multiple gestation delays

Stability Switches and Hopf Bifurcation Induced by Nutrient Recycling Delay in a Reaction‐Diffusion Nutrient‐Phytoplankton Model

“…(23) □ rough the above analysis and motivated by Corollary 2.4 of Ruan and Wei in [28], we can establish the distribution of roots of characteristic equation (11) in the case of n � 0.…”

“…01 < τ − 00 , then all roots of (11) have negative real parts for τ ∈ [0, τ + 00 ); equation (11) has a pair of purely imaginary roots and other roots have negative real parts for τ � τ + 00 ; equation (11) has at least a root with positive real part for τ > τ + 00 . (ii) If τ + 01 > τ − 00 , then there exists a positive integer k such that all roots of (11) have negative real parts for τ…”

“…It is found that inclusion of nutrient recycling enhances the chances of recurring bloom dynamics. After that, some expanded models were investigated by incorporating zooplankton population in [7][8][9][10][11].…”

“…Moreover, equation (20) has two positive real roots under the assumption (H6). us, characteristic equation (11) has two pairs of purely imaginary roots λ � ± iω ± n , where…”

Dynamical Study of an Eco-Epidemiological Delay Model for Plankton System with Toxicity

“…Thakur et al. ( 2020 ) have established the plankton-fish model under the consequence of multiple gestation delays and demonstrated that the two equal gestation delays may promote the chaotic phenomenon in the plankton system.…”