Abstract—A dynamical model for toxin producing phytoplankton and zooplankton has been formulated and analyzed. Due to gestation of prey, a discrete time delay is incorporated in the predator dynamics. The stability of the delay model is discussed and Hopf-bifurcation to a periodic orbit is established. To substantiate analytical findings, numerical simulations are performed. The system shows rich dynamic behavior including chaos and limit cycles.
Index Terms—Chaos, hopf bifurcation, periodic solution, time delay.
Anuraj Singh is with Graphic Era University, Dehradun 248002, Uttrakhand, India (e-mail: anurajiitr@gmail.com).
Sunita Gakkhar is with India Institute of Technology Roorkee, Roorkee 247667, Uttrakhand, India. (e-mail: sungkfma@iitr.ernet.in).
Cite: Anuraj Singh and Sunita Gakkhar, "Analysis of Delayed Toxin Producing Phytoplankton-Zooplankton System," International Journal of Modeling and Optimization vol. 2, no. 6, pp. 677-680, 2012.
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