Diffusive Three Species Plankton Model in the Presence of Toxic Prey: Application to Sundarban Mangrove Wetland

Abstract

The bloom of toxin producing phytoplankton (TPP) is an environmental issue due to its negative impact on fresh water and marine ecology. In this paper, such a phenomenon is modeled using the reaction–diffusion equations. The spatiotemporal interaction among non-toxin producing phytoplankton (NTP), TPP, and zooplankton has been considered with Holling type II and III functional responses. The stability analysis for non-spatial and spatial model system is carried out and numerical simulations are performed for a fixed set of parameter values, which is realistic to planktonic dynamics. It has been observed that on increasing the reduction rate of zooplankton, the system shows cyclic to stable behavior. The result shows that the predators which avoid to toxic prey promote the bloom. Non-Turing patchy pattern has also been observed on time evolution. In this work, we have taken the case study of Sundarban mangrove wetland which is suffering from algal bloom due to the presence of toxic Dinoflagellates and Cyanophyceae. Through the numerical simulation, it has been shown that the higher value of reduction rate of zooplankton ([Formula: see text]) is responsible for bad health of the wetland system.

Dynamical study of infochemical influences on tropic interaction of diffusive plankton system

“…Assuming spatial variability in the form of diffusion fascinated our study. (ii) Thakur et al [11] investigated a diffusion-based competing plankton system for Sundarban mangrove system and mainly focused on the role of reduction rate of zooplankton, but infochemical term in phytoplankton has been ignored in the model formulation. Therefore, this term has been taken in the third equation of the system (2.1).…”

“…Resulting grazing-induced release of infochemical in multi-tropic interaction attracts carnivorous predators that reduce the grazing pressure on primary producer [6]. Recently, the models investigating the effect of toxin-producing phytoplankton (TPP) received much attention [7][8][9][10][11]. But grazing-induced toxic deterrents have received less attention.…”

“…Sekerci and Petrovskii [23] studied the oxygen-plankton model system in pattern formation and observed (for somewhat different initial conditions) irregular spatiotemporal patterns, simple spirals, double spirals or "mushroom-like" structures and "snake-like" structures. Thakur et al [11] have proposed diffusive three species plankton models with toxic effect for wetland ecosystem. Chaudhuri et al [24] studied toxic phytoplankton-induced spatiotemporal patterns observed that the populations become inhomogeneous in the presence of toxin-producing phytoplankton.…”

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

“…For simplicity, we specify the spatial location as an interval Ω � (0, π), where π denotes the depth of the water column and can be changed into any depth through a suitable transformation. Moreover, some other nutrient-plankton models incorporating spatial effects are investigated in [16][17][18][19][20][21].…”

“…From D n � A n + B and B < 0, it can be found that D n > 0 implies A n − B > 0. 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…”