Pseudo almost periodic solutions and global exponential stability of a new class of nonlinear generalized Gilpin-Ayala competitive model with feedback control with delays. (English) Zbl 1476.34149
Summary: 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.
MSC:
| 34K14 | Almost and pseudo-almost periodic solutions to functional-differential equations |
| 00A72 | General theory of simulation |
| 34K35 | Control problems for functional-differential equations |
Keywords:
pseudo almost periodic solution; Gilpin-Ayala competitive model; feedback control; Krasnoselskii’s fixed point theorem; global exponential stabilityReferences:
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