Abstract

Abstract A stochastic mutualism model is proposed and investigated in this paper. We show that there is a unique solution to the model for any positive initial value. Moreover, we show that the solution is stochastically bounded, uniformly continuous and globally attractive. Under some conditions, we conclude that the stochastic model is stochastically permanent and persistent in mean. Finally, we introduce some figures to illustrate our main results.

Highlights

  • Population systems have long been an important theme in mathematical biology due to their universal existence and importance

  • Since stochastic differential equation ( ) describes population dynamics, it is necessary for the solution of the system to be positive and not to explode to infinity in a finite time

  • 2.4 Global attractivity Here we show that the solution of ( ) is globally attractive

Read more

Summary

Introduction

Population systems have long been an important theme in mathematical biology due to their universal existence and importance. The above model is not so good in describing the mutualism of two species (see [ ]). As a matter of fact, population systems are often subject to environmental noise, i.e., due to environmental fluctuations, parameters involved in population models are not absolute constants, and they may fluctuate around some average values Based on these factors, more and more people began to be concerned about stochastic population systems (see [ – ]). Since stochastic differential equation ( ) describes population dynamics, it is necessary for the solution of the system to be positive and not to explode to infinity in a finite time.

Positive and global solution
Conclusions

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.