# Mathematical model of fish, birds and tourists in wetlands: the impact of periodic fluctuations on the coexistence of species

Article

## Abstract

The present paper deals with a harvested predator–prey model and the dynamics of tourists in wetlands. This model describes the coexistence and extinction of at least one of the species in the wetlands. By the Mahwin continuation theorem of coincidence degree theory, we prove the existence of a positive periodic solution (in place of an equilibrium) provided that the harvest rate of prey is in a suitable range. Further, by constructing a suitable Lyapunov functional, we obtain sufficient conditions for global asymptotic stability of the positive periodic solution. Finally numerical simulations are carried out to illustrate the feasibility of the mathematical results.

## Keywords

Predator–prey Permanence Periodic solution Stability Tourism

## Mathematics Subject Classification

92D25 34D23 39A25

## Notes

### Acknowledgements

Authors are really grateful to the editor and referees for their careful, comments and helpful suggestions. Funding was provided by UMISCO and the International Sciences Programme.

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