Population Dynamics and Pattern Formation in an Info-chemical Mediated Tri-trophic Plankton Model

In this thesis, we study a spatio–temporal prey–predator model of plankton. This model has spatial interaction terms which represent a plankton dynamics that includes info–chemical mediated trophic interactions. We consider both a simplified two species model which has been studied in the literature (mostly in biological terms) and an extended, four-species model. In the latter, the grazing pressure of microzooplankton (M) on phytoplankton (P) is controlled through external infochemical (C) mediated predation by copepods (Z). We undertake a stability analysis of both the two species model and the four species model and compare the system dynamics. In relation to this, the critical conditions for Turing instability are derived; these are necessary and sufficient. Furthermore, we consider the degenerated situation wherein Turing bifurcation and Hopf bifurcation occur simultaneously. We also consider under what conditions Turing patterns are exhibited and under what conditions spatiotemporal patterns are observed generally. The Transient Turing instability of spatial interactions –exhibited by the two species model–is introduced and investigated in a number of ways. We also study the effects of the paradox of enrichment. This paradox led to a loss of stability in the four species model after this was derived from the two species model by expansion and by the addition of resources. Further, a numerical continuation technique was used to determine the existence of multiple stationary patterns

Bloom Formation and Turing Patterns in an Infochemical Mediated Multitrophic Plankton Model

A two-species predator–prey plankton model is studied, where the grazing pressure of microzooplankton on phytoplankton is controlled through external infochemical mediated predation. The system stability is analyzed in order to explain the conditions for phytoplankton bloom formation and to explore system bifurcations. The interplay between the level of infochemical-mediated external predation and the phytoplankton carrying capacity is considered over a range of parameter values and the resultant system dynamics is illustrated. The model is extended to include a spatial diffusion term leading to a reaction–diffusion system that is investigated by determining the Turing space of the model. Thereafter, the bifurcation analysis of specific time-independent patterns is explored. Through time integration, the system is also shown to exhibit the potential for temporally varying spatial patterns

Pattern formation in PMZC plankton model

In this paper, we focus on the phenomenon of pattern formation in a reaction diffusion model of plankton dynamics which includes support for infochemically mediated trophic interactions. We consider a four species model created on the basis of the two species models which have been studied previously. In our model, which is an extended version of these previous models, the grazing pressure of microzooplankton (M) on phytoplankton (P) is controlled through external infochemically (C) mediated predation by copepods (Z). We undertake a stability analysis of both the two species and the four species models and compare their system dynamics. We compared the mathematical roots related to these models using both numerical and analytical methods, and we found consistency between the two approaches using asymptotic expansion. We also explored spatial pattern formation in relation to both forms of model and considered under what conditions Turing patterns are exhibited and when spatiotemporal chaos can be observed. An attempt was made to study the non-Turing patterns which were discovered with a special emphasis on spatiotemporal chaos