Abstract. In this paper, we investigate the complex dynamics of a spatial plankton-fish system with Holling type III functional responses. We have carried out the analytical study for both one and two dimensional system in details and found out a condition for diffusive instability of a locally stable equilibrium. Furthermore, we present a theoretical analysis of processes of pattern formation that involves organism distribution and their interaction of spatially distributed population with local diffusion. The results of numerical simulations reveal that, on increasing the value of the fish predation rates, the sequences spots → spot-stripe mixtures→ stripes→ hole-stripe mixtures holes→ wave pattern is observed. Our study shows that the spatially extended model system has not only more complex dynamic patterns in the space, but also has spiral waves.

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The paper is devoted to a reaction-diffusion system of equations describing phytoplankton and zooplankton distributions. Linear stability analysis of the model is carried out. Turing and Hopf stability boundaries are found. Emergence of two-dimensional spatial structures is illustrated by numerical simulations. Travelling waves between various stationary solutions are investigated. Transitions between homogeneous in space stationary solutions and Turing structures are studied.

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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.

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In this paper, we have investigated a model with three interacting species: non-toxic phytoplankton, toxic phytoplankton and zooplankton with Holling type II and III functional responses over the space and time. The role of toxin producing phytoplankton (TPP) has been studied. We have presented the theoretical analysis of pattern formation in spatially distributed population with local diffusion. The paper highlights the heterogeneity of HABs over space and time. The choice of parameter values and the functional response is important to study the effect of TPP, also it would depend more on the nonlinearity of the system. With the help of numerical simulations, we have observed the spatial and spatiotemporal patterns for plankton system. This study demonstrates that TPP plays an important role in controlling the dynamics. We have observed that prey’s anti-predator efforts promote predator switching. It has been found that high predation of TPP helps for the coexistence of toxic, non-toxic phytoplankton and zooplankton population.