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

• Published in: Nonlinear dynamics Vol. 84; no. 3; pp. 1569 - 1594
• Main Authors: Biswas, Santanu, Saifuddin, Md, Sasmal, Sourav Kumar, Samanta, Sudip, Pal, Nikhil, Ababneh, Faisal, Chattopadhyay, Joydev
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.05.2016; Springer Nature B.V
• Subjects: Automotive Engineering; Chaos theory; Classical Mechanics; Computer simulation; Control; Delay; Differential equations; Dynamical Systems; Engineering; Epidemiology; Gestation; Hopf bifurcation; Liapunov exponents; Mathematical analysis; Mathematical models; Mechanical Engineering; Nonlinear analysis; Nonlinear dynamics; Original Paper; Parameters; Population growth; Predator-prey simulation; Response time; Time lag; Vibration; Chaos; Stability analysis; Eco-epidemiology; Time delay; Hopf bifurcation; Allee effect
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-015-2589-9

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.