Dynamical Complexity in Some Ecological Models: Effects of Toxin Production by Phytoplankton
R. K. K. Upadhyay
Indian School of Mines University, India
R. K. K. Naji
University of Baghdad, Iraq
N. Kumari
Indian School of Mines University, India
Published 2007-01-25


dynamical complexity
toxin producing phytoplankton
chaotic dynamics
functional response
specialist predator
generalist predator

How to Cite

Upadhyay, R.K.K., Naji, R.K.K. and Kumari, N. (trans.) (2007) “Dynamical Complexity in Some Ecological Models: Effects of Toxin Production by Phytoplankton”, Nonlinear Analysis: Modelling and Control, 12(1), pp. 123–138. doi:10.15388/NA.2007.12.1.14726.


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.