Permanence and Uniformly Asymptotic Stability of Almost Periodic Positive Solutions for a Dynamic Commensalism Model on Time Scales

Subject Areas : International Journal of Mathematical Modelling & Computations

Mahammad Khuddush ¹ , Kapula Rajendra Prasad ² , K. V. Vidyasagar ³

1 - Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam, India-530003
2 - Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam, India-530003
3 - Department of Applied Mathematics, College of Science and Technology, Andhra University, Visakhapatnam, India-530003

Received: 2019-12-15 Accepted : 2020-03-02 Published : 2020-03-01

Keywords: Time scales, commensalism model, almost periodic solution, Uniform asymptotic stability‎,

Abstract :

In this paper, we study dynamic commensalism model with nonmonotic functional response, density dependent birth rates on time scales and derive sufficient conditions for the permanence. We also establish the existence and uniform asymptotic stability of unique almost periodic positive solution of the model by using Lyapunov functional method.