Abstract
We investigate dynamical complexities in two types of chaotic tri-trophic aquatic food-chain model systems representing a real situation in the marine environment. Phytoplankton produce chemical substances known as toxins to reduce grazing pressure by zooplankton [1]. The role of toxin producing phytoplankton (TPP) on the chaotic behavior in these food chain systems is investigated. Holling type I, II, and III functional response forms are considered to study the interference between phytoplankton and zooplankton populations in the presence of toxic chemical. Our study shows that chaotic dynamics is robust to changes in the rates of toxin release as well as the toxin release functions. The present study also reveals that the rate of toxin production by toxin producing phytoplankton plays an important role in controlling oscillations in the plankton system. The different mortality functions of zooplankton due to toxin producing phytoplankton have significant influence in controlling oscillations, coexistence, survival or extinction of the zooplankton population. Further studies are needed to ascertain if this defence mechanism suppresses chaotic dynamics in model aquatic systems.
Highlights
It is a challenge to understand the dynamical complexities of an ecological system
According to the above discussion for the dynamical behavior of model system (1) and model system (2), it is clear that increasing the strength of toxic chemical released by toxin producing phytoplankton (TPP) population reduce the prevalence of chaos, our observation is that the toxin released by TPP population acts as a bio-control by changing the state of chaos to order
The rate of toxic substance released by TPP is to be high for type I functional form than those of type II and type III functional form
Summary
It is a challenge to understand the dynamical complexities of an ecological system. Field and laboratory studies are hard to design and implement. It has been shown that the toxin production by phytoplankton suppresses chaotic dynamics [11, 12] These authors added an extramortality term to the rate equation for the middle predator in the Hastings and Powell model [9] and Upadhyay and Rai model [8] to incorporate the effect of toxin release by phytoplankton. One of the main objectives of our study is to investigate how dynamical complexities of a model given by Upadhyay and Rai [8] and Hasting and Powell [9] changes their basic character in response to different types of toxin release functions. It is observed that toxin producing phytoplankton (TPP) population do not release toxic chemical always, release only in the presence of dense zooplankton population around it This phenomenon has been included in the interaction of Holling type I and Dynamical Complexity in Some Ecological Models type II functional form respectively.
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