The Impact of Anti-Predator Behavior and Toxicant on An Ecological Neutrosophic Model
Huda Salah Kareem *1, Aseel Amer Abd 2
1 College of Engineering, Iraqi University and Electrial Engineering Technology College , Middle Technical University, Iraq
2 College of Engineering, Iraqi University and Electrial Engineering Technology College , Middle Technical University, Iraq
Emails: huda.s.kareem@aliraqia.edu.iq; aseel_amer2@mtu.edu.iq
Abstract
This paper discusses a neutrosophic mathematical model consisting of three nonlinear ordinary differential equations describing the interaction between two prey and a predator with the use of function response Holling's type IV and Lotka Volttra. It appears that the first prey has a way to defend itself by using the toxic substance directly to the predator, as well as the effect of the predator on the toxic substance. The conditions for the existence of the solution and the uniqueness of the boundaries were discussed, and then the different equilibrium points and the stability of the system around the equilibrium points were analyzed. The Lyapunov function was used to study the global dynamics of this proposed model. Finally, numerical simulations were performed to show the analytical results.
Keywords: Prey- Predator; Holling's type IV Function Response; Toxicity; Anti-Predator; neutrosophic model