Pseudo almost periodic solutions and global exponential stability of a new class of nonlinear generalized Gilpin–Ayala competitive model with feedback control with delays

Results of this paper discuss a new class of nonlinear generalized Gilpin–Ayala competitive model with feedback control. Prior to the main results and using different approach, we prove the uniformly permanence of the solutions of the proposed model. Moreover, we study the existence of pseudo almost periodic solutions via the technique of Krasnoselskii’s fixed point Theorem. By constructing an appropriate Lyapunov function, we discuss the globally exponential stability of the pseudo almost periodic solutions. To demonstrate the validity of the theoretical findings, we present a numerical example associated with a graphical representation. The advantage of our results are verified by a comparison session at the end of the paper.