Complex dynamics of an eco-epidemiological model with different competition coefficients and weak Allee in the predator

• Published in: Chaos, solitons and fractals Vol. 91; pp. 270 - 285
• Main Authors: Saifuddin, Md, Biswas, Santanu, Samanta, Sudip, Sarkar, Susmita, Chattopadhyay, Joydev
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2016
• Subjects: Bifurcation analysis; Chaos; Eco-epidemiological system; Emergent carrying capacity; Lyapunov exponent; Weak Allee; Chaos; Weak Allee; Emergent carrying capacity; Eco-epidemiological system; Bifurcation analysis; Lyapunov exponent
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2016.06.009

The paper explores an eco-epidemiological model with weak Allee in predator, and the disease in the prey population. We consider a predator-prey model with type II functional response. The curiosity of this paper is to consider different competition coefficients within the prey population, which leads to the emergent carrying capacity. We perform the local and global stability analysis of the equilibrium points and the Hopf bifurcation analysis around the endemic equilibrium point. Further we pay attention to the chaotic dynamics which is produced by disease. Our numerical simulations reveal that the three species eco-epidemiological system without weak-Allee induced chaos from stable focus for increasing the force of infection, whereas in the presence of the weak-Allee effect, it exhibits stable solution. We conclude that chaotic dynamics can be controlled by the Allee parameter as well as the competition coefficients. We apply basic tools of non-linear dynamics such as Poincare section and maximum Lyapunov exponent to identify chaotic behavior of the system.