Refugia and Allee Effect in Prey Species Stabilize Chaos in a Tri-Trophic Food Chain Model

• Published in: Differential equations and dynamical systems Vol. 30; no. 3; pp. 631 - 657
• Main Authors: Nath, Binayak, Kumari, Nitu, Kumar, Vikas, Das, Krishna Pada
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.07.2022; Springer Nature B.V
• Subjects: Computer Science; Engineering; Food chains; Mathematical models; Mathematics; Mathematics and Statistics; Original Research; Saturation; Stability criteria; Permanence and non-permanence; Direction of Hopf bifurcation; Hopf bifurcation; Global stability; Tri-trophic food chain; Local stability
• ISSN: 0971-3514; 0974-6870
• DOI: 10.1007/s12591-019-00457-z

In this paper a mathematical model is proposed and analyzed to study the dynamics of tri-trophic food chain model with refugia and allee effect in prey species. Criteria for local stability, instability and global stability of the non-negative equlibria are obtained. Different conditions for the coexistence of equilibrium solutions are discussed. Persistence, permanence of the system and global stability of the positive interior equilibrium solution are discussed. Further we pay attention to the chaotic dynamics which is produced by half-saturation constant. Our numerical simulations reveal that the three species food chain model without refugia and allee effect induced chaos from stable focus for increasing the value of half-saturation constant. We conclude that chaotic dynamics can be controlled by the Allee and refugia parameters.