A delayed prey–predator system with prey subject to the strong Allee effect and disease

Santanu Biswas, Md Saifuddin, Sourav Kumar Sasmal, Sudip Samanta, Nikhil Pal, Faisal Ababneh, Joydev Chattopadhyay

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

In this article, an eco-epidemiological model with strong Allee effect in prey population growth is presented by a system of delay differential equations. The time lag in terms of the delay parameter corresponds to the predator gestation period. We inspect elementary mathematical characteristic of the proposed model such as uniform persistence, stability and Hopf bifurcation at the interior equilibrium point of the system. We execute several numerical simulations to illustrate the proposed mathematical model and our analytical findings. We use basic tools of nonlinear dynamic analysis as first return maps, Poincare sections and Lyapunov exponents to identify chaotic behavior of the system. We observe that the system exhibits chaotic oscillation due to the increase of the delay parameter. Such chaotic behavior can be suppressed by the strength of Allee effect.

Original languageEnglish
Pages (from-to)1569-1594
Number of pages26
JournalNonlinear Dynamics
Volume84
Issue number3
DOIs
Publication statusPublished - May 1 2016

Fingerprint

Prey-predator
Allee Effect
Prey
Hopf bifurcation
Chaotic systems
Chaotic Behavior
Dynamic analysis
Differential equations
Uniform Persistence
Mathematical models
Epidemiological Model
Poincaré Section
Return Map
Population Growth
Time Lag
Computer simulation
Interior Point
Predator
Delay Differential Equations
Nonlinear Analysis

Keywords

  • Allee effect
  • Chaos
  • Eco-epidemiology
  • Hopf bifurcation
  • Stability analysis
  • Time delay

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this

Biswas, S., Saifuddin, M., Sasmal, S. K., Samanta, S., Pal, N., Ababneh, F., & Chattopadhyay, J. (2016). A delayed prey–predator system with prey subject to the strong Allee effect and disease. Nonlinear Dynamics, 84(3), 1569-1594. https://doi.org/10.1007/s11071-015-2589-9

A delayed prey–predator system with prey subject to the strong Allee effect and disease. / Biswas, Santanu; Saifuddin, Md; Sasmal, Sourav Kumar; Samanta, Sudip; Pal, Nikhil; Ababneh, Faisal; Chattopadhyay, Joydev.

In: Nonlinear Dynamics, Vol. 84, No. 3, 01.05.2016, p. 1569-1594.

Research output: Contribution to journalArticle

Biswas, S, Saifuddin, M, Sasmal, SK, Samanta, S, Pal, N, Ababneh, F & Chattopadhyay, J 2016, 'A delayed prey–predator system with prey subject to the strong Allee effect and disease', Nonlinear Dynamics, vol. 84, no. 3, pp. 1569-1594. https://doi.org/10.1007/s11071-015-2589-9
Biswas, Santanu ; Saifuddin, Md ; Sasmal, Sourav Kumar ; Samanta, Sudip ; Pal, Nikhil ; Ababneh, Faisal ; Chattopadhyay, Joydev. / A delayed prey–predator system with prey subject to the strong Allee effect and disease. In: Nonlinear Dynamics. 2016 ; Vol. 84, No. 3. pp. 1569-1594.
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