STOCHASTIC AND DELAY ANALYSIS OF TWO PREYS AND ONE PREDATOR ECOLOGICAL SYSTEM WITH COMPETITION AMONG PREYS AND SELF INTERACTION

In this research article, a two prey-one predator system with intra specific competition and self-interaction is investigated and its dynamics are mathematically analyzed. The positivity of the solution and boundedness of the system is studied. The occurrence of possible equilibrium points and stability of the system at those points is examined. The necessary and sufficient condition for the existence of positive interior equilibrium point $E_ 6 (x^∗ , y^∗ , z^∗ )$ is obtained. Also the point $E_6 (x^∗ , y^∗ , z^∗ )$ is investigated for the local and global stability of the system. Stability of the delayed model is investigated and it is observed that stability of the system is dependent on time delay. Time delay drives the system from stable to unstable state. The system and its value is described by environmental stochasticity in the form of Gaussian white noise. Numerical simulation is  performed to justify the analytical findings.

 

Editorial remark [2018-03-12]: The article has been replaced according authors request. The old version of article is available here.