A study of dynamical syn-eco symbiotic system with bio-economic aspect at interior equilibrium

Abstract

This paper proposes a multi species ecosystem with optimal harvesting of the prey (S1), and Super predator (S3).The predator (S2) is surviving on the prey and the super predator is surviving on predator. The mathematical model is defined by three non-linear ordinary differential equations .The existence of bionomic equilibrium of the system has been discussed. The Local stability is discussed using Routh-Hurwitz‘s criteria and global stability by Lyapunov’s function. The analytical stability criteria are supported by numerical simulations using Mat lab.