Rich dynamics of non-toxic phytoplankton, toxic phytoplankton and zooplankton system with multiple gestation delays

  • Ashok MondalEmail author
  • A. K. Pal
  • G. P. Samanta


The plankton community is classified into three category of species, namely, non-toxic phytoplankton (NTP), toxic phytoplankton (TPP) and zooplankton. In this work we have introduced a mathematical model for the interaction of NTP, TPP and zooplankton population in an open marine system. We have incorporated two time delays and observed important mathematical characteristics of the proposed model such as positivity, boundedness, stability and Hopf-bifurcation for all possible combinations of both the delays at the interior equilibrium point of the model system. It is noted that increase in gestation delay may lead to the destabilization of stationary points through the creation of limit cycles. Various numerical simulations are performed to validate the analytical findings obtained here.


Phytoplankton Zooplankton Stability Permanence Hopf-bifurcation 



The authors are grateful to the anonymous referees and Editor in Chief Prof. Jian-Qiao Sun for their careful reading, valuable comments and helpful suggestions, which have helped them to improve the presentation of this work significantly. The first author (Ashok Mondal) is thankful to the University Grants Commission, India for providing SRF (RGNF). The second author (A. K. Pal) acknowledges financial support from UGC, India (MRP No.-PSW-128/15-16 (ERO)).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Engineering Science and Technology, ShibpurHowrahIndia
  2. 2.Department of MathematicsS. A. Jaipuria CollegeKolkataIndia

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