Sistem Parametrelerinin Plankton Dinamiği Üzerine Etkisi: Matematiksel Modelleme Yaklaşımı

Fitoplankton-zooplankton modeli oksijen-plankton modelinin bir alt modeli olarak önerilmiş ve analiz edilmiştir. Matematiksel olarak, ikili diferensiyel denklem yapısı dikkate alınmıştır. Bu çalışmada, okyanuslardaki fitoplanktonlar tarafından fotosentez işleminin sonucu olarak üretilen oksijen oranı, kararlı olduğu varsayılarak oksijen konsantrasyonu sabit bir değer olarak seçilmiştir. Sistem parametrelerindeki değişim etkisi altındaki fitoplankton-zooplankton popülasyonunun temel özellikleri, analitik ve nümerik yöntemlerle detaylandırılmıştır. Özellikle, zooplanktonun büyüme hızı ve fitoplankton için tür içi rekabetin sistem davranışı üzerindeki etkileri ele alınmıştır. Sistemin zamana bağlı değişimini görmek için, mekâna bağlı olmayan sistem ele alınmıştır. Sonrasında ise mekânsal sistem, çok sayıdaki sayısal simülasyonlar yardımıyla calışılmıştır. Mevcut model sisteminin hem zamana hem de mekâna bağlı olduğu durumda zengin dinamiğe sahip olduğu görülmüştür.

Anahtar Kelimeler:

Fitoplankton-zooplankton, Matematiksel modelleme, Yapı oluşumu

Effect of System Parameters on Plankton Dynamics: A Mathematical Modelling Approach

A phytoplankton-zooplankton model is proposed and analyzed as a submodel of oxygen-plankton model. Mathematically, two coupled differential equations are considered. In this work, oxygen which is produced as a result of photosynthetic process by phytoplankton in ocean is assumed stable by keep oxygen concentration as a constant value. Basic properties of the phytoplankton-zooplankton population are detailed with analytical and numerical way under the effect of change in system parameters. In particular, effects of per-capita growth rate of zooplankton and intraspecific competition for phytoplankton on the systems’ dynamical behavior are considered. To understand the system temporal structure nonspatial system is detailed. Then the spatial case is focussed with the assist of extensive numerical simulations. It is observed that the model system has rich patterns in both temporal and spatial case.

Keywords:

Phytoplankton-zooplankton, Mathematical modelling, Pattern formation,

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