Pattern Formation in Models of Plankton–Fish Dynamics in a Noisy

Chaos and fractals in fish school motion, I., Chaos, Solitons & Frac- tals, 12(2), 277-288. [6] Tikhonov, D.A. & H. Malchow, 2003, Chaos and fractals in fish school.
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AICME II abstracts

Spatio-Temporal Complexity in Population Dynamics

Spatio-Temporal Complexity in Population Dynamics

AICME II abstracts

References Pattern Formation in Models of Plankton–Fish Dynamics in a Noisy and Patchy Environment

[1] Scheffer, M., 1991, Fish and nutrients interplay determines algal biomass: a minimal model, OIKOS, 62, 271-282.

Horst Malchow1 , Dmitry A. Tikhonov2 , Alexander B. Medvinsky3 and Sergei V. Petrovskii4 .

[2] Malchow, H., 1993, Spatio-temporal pattern formation in nonlinear nonequilibrium plankton dynamics, Proc. R. Soc. Lond. B, 251, 103109.

The impacts of variable planktivorous fish and noisy zooplankton mortality on phytoplankton-zooplankton interactions are described, using a minimal model of the nutrients-plankton-fish food chain [1, 2]. Locally, the influence of external forcing of planktonic predator-prey oscillations by fish school invasions and feeding is investigated. The space is divided into patches of different phytoplankton growth [3]. The effects of mobile fish schools on the plankton dynamics are described. The plankton growth, interactions and transport are modelled with reaction-diffusion equations whereas the fish school motion is discrete and rule-based, depending on the local zooplankton density as well as on spatial position, previous direction and residence time [4]. The fractal characteristics of the fish school motion are analysed [5, 6]. The emergence of stationary and travelling plankton population waves is presented. It is shown that not only cruising and feeding planktivorous fish schools but also noise can induce the planktonic patchiness.

[3] Malchow, H., S.V. Petrovskii & A.B. Medvinsky, 2002, Numerical study of plankton-fish dynamics in a spatially structured and noisy environment, Ecol. Model., 149, 247-255. [4] Malchow, H., B. Radtke, M. Kallache, A.B. Medvinsky, D.A. Tikhonov & S.V. Petrovskii, 2000, Spatio-temporal pattern formation in coupled models of plankton dynamics and fish school motion, Nonlinear Analysis: Real World Applications 1, 53-67. [5] Tikhonov, D.A., J. Enderlein, H. Malchow & A.B. Medvinsky, 2001, Chaos and fractals in fish school motion, I., Chaos, Solitons & Fractals, 12(2), 277-288. [6] Tikhonov, D.A. & H. Malchow, 2003, Chaos and fractals in fish school motion, II., Chaos, Solitons & Fractals, 16(2), 287-289.

1

Institute for Environmental Systems Research, Department of Mathematics and Computer Science, University of Osnabr¨ uck, D-49069 Osnabr¨ uck, Germany (e-mail: [email protected]). 2 Institute for Mathematical Problems of Biology, Russian Academy of Sciences, Pushchino, Moscow Region, 142290, Russia (e-mail: [email protected]). 3 Institute for Theoretical & Experimental Biophysics, Russian Academy of Sciences, Pushchino, Moscow Region, 142290, Russia (e-mail: [email protected]). 4 Shirshov Institute of Oceanology, Russian Academy of Science, Nakhimovsky Prospekt 36, Moscow 117218, Russia (e-mail: [email protected]).

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