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Spatiotemporal Pattern Formation in a Prey-Predator System: The Case Study of Short-Term Interactions Between Diatom Microalgae and Microcrustaceans

1
Southern Scientific Centre of the Russian Academy of Sciences (SSC RAS), Chekhov Street, 41, Rostov-on-Don 344006, Russia
2
Faculty of IT Systems and Technologies, Don State Technical University (DSTU), Gagarin Square, 1, Rostov-on-Don 344000, Russia
3
Faculty of Biology, Lomonosov Moscow State University (MSU), Leninskie Gory, 1-12, Moscow 119991, Russia
4
Shirshov Institute of Oceanology, Russian Academy of Sciences, Nakhimovskiy Prospekt, 36, Moscow 117218, Russia
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(7), 1065; https://doi.org/10.3390/math8071065
Received: 16 May 2020 / Revised: 19 June 2020 / Accepted: 23 June 2020 / Published: 1 July 2020
A simple mathematical model capable of reproducing formation of small-scale spatial structures in prey–predator system is presented. The migration activity of predators is assumed to be determined by the degree of their satiation. The hungrier individual predators migrate more frequently, randomly changing their spatial position. It has previously been demonstrated that such an individual response to local feeding conditions leads to prey–taxis and emergence of complex spatiotemporal dynamics at population level, including periodic, quasi-periodic and chaotic regimes. The proposed taxis–diffusion–reaction model is applied to describe the trophic interactions in system consisting of benthic diatom microalgae and harpacticoid copepods. The analytical condition for the oscillatory instability of the homogeneous stationary state of species coexistence is given. The model parameters are identified on the basis of field observation data and knowledge on the species ecology in order to explain micro-scale spatial patterns of these organisms, which still remain obscure, and to reproduce in numerical simulations characteristic size and the expected lifetime of density patches.
Keywords: taxis-diffusion-reaction; Patlak-Keller-Segel model; indirect prey-taxis; cross-diffusion; chaos; pattern formation taxis-diffusion-reaction; Patlak-Keller-Segel model; indirect prey-taxis; cross-diffusion; chaos; pattern formation
MDPI and ACS Style

Tyutyunov, Y.V.; Zagrebneva, A.D.; Azovsky, A.I. Spatiotemporal Pattern Formation in a Prey-Predator System: The Case Study of Short-Term Interactions Between Diatom Microalgae and Microcrustaceans. Mathematics 2020, 8, 1065.

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