Dynamic relationship between the mutual interference and gestation delays of a hybrid tritrophic food chain model


  • Rashmi Agrawal Department of Humanities and Science, S R Engineering College, Warangal, Telangana 506371.
  • Debaldev Jana Department of Mathematics and SRM Research Institute, SRM Institute of Science and Technology, Kattankulathur 603203, Tamil Nadu.
  • Ranjit Kumar Upadhyay Department of Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad, Jharkhand 826004.
  • V. Sree Hari Rao Turnin Innovation Technologies (Pvt) Ltd., Hyderabad.




CM functional response, BD functional response, HV functional response, gestation delay, multiple time delays, Hopf-bifurcation, chaos.


We have proposed a three-species hybrid food chain model with multiple time delays. The interaction between the prey and the middle predator follows Holling type (HT) II functional response, while the interaction between the top predator and its only food, the middle predator, is taken as a general functional response with the mutual interference schemes, such as Crowley–Martin (CM), Beddington–DeAngelis (BD) and Hassell– Varley (HV) functional responses. We analyse the model system which employs HT II and CM functional responses, and discuss the local and global stability analyses of the coexisting equilibrium solution. The effect of gestation delay on both the middle and top predator has been studied. The dynamics of model systems are affected by both factors: gestation delay and the form of functional responses considered. The theoretical results are supported by appropriate numerical simulations, and bifurcation diagrams are obtained for biologically feasible parameter values. It is interesting from the application point of view to show how an individual delay changes the dynamics of the model system depending on the form of functional response. doi:10.1017/S144618111700044X

Author Biography

V. Sree Hari Rao, Turnin Innovation Technologies (Pvt) Ltd., Hyderabad.

CEO, Turnin Innovation Technologies (Pvt) Ltd., Hyderabad.





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