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The stationary distribution and ergodicity of a stochastic mutualism model

  • Jingliang Lv EMAIL logo , Sirun Liu and Heng Liu
Published/Copyright: May 18, 2018
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 68 Issue 3

Abstract

This paper is concerned with a stochastic mutualism system with toxicant substances and saturation terms. We obtain the sufficient conditions for the existence of a unique stationary distribution to the equation and it has an ergodic property. It is interesting and surprising that toxicant substances have no effect on the stationary distribution of the stochastic model. Simulations are also carried out to confirm our analytical results.

MSC 2010: Primary 60H10, 60G10
Keywords: mutualism model; ergodicity; stationary distribution

This work was supported by the National Natural Science Foundation of P. R. China (No.11501148), Shandong Provincial Natural Science Foundation, China (No.ZR2015AQ002).

Communicated by Gejza Wimmer

Acknowledgement

We are grateful to the anonymous referee for his careful reading and helpful suggestions which led to an improvement of our original manuscript.

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Received: 2016-8-16
Accepted: 2017-2-1
Published Online: 2018-5-18
Published in Print: 2018-6-26

© 2018 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2017-0135
Keywords for this article
mutualism model; ergodicity; stationary distribution

Articles in the same Issue

  2. Small-large subgroups of the reals
  4. Structural properties of algebras of S-probabilities
  6. Approximation in quantum measure spaces
  8. On Fibonomial sums identities with special sign functions: analytically q-calculus approach
  10. On the proximity of multiplicative functions to the number of distinct prime factors function
  12. Truncated euler polynomials
  14. Growth series of crossed and two-sided crossed products of cyclic groups
  16. Weakly U-abundant semigroups with strong Ehresmann transversals
  18. Iterative learning control with pulse compensation for fractional differential systems
  20. Rectifiable and nonrectifiable solution curves of half-linear differential systems
  22. Uniqueness properties of meromorphic functions in the light of three shared sets
  24. A new family of analytic functions defined by means of Rodrigues type formula
  26. Perturbation analysis of a nonlinear equation arising in the Schaefer-Schwartz model of interest rates
  28. On the solutions of a second-order difference equation in terms of generalized Padovan sequences
  30. Fixed points in C∗-algebra valued b-metric spaces endowed with a graph
  32. A general fixed point theorem for two pairs of mappings satisfying a mixed implicit relation
  34. Productively sequential spaces
  36. Euler classes of vector bundles over iterated suspensions of real projective spaces
  38. The stationary distribution and ergodicity of a stochastic mutualism model
  40. Restricted injective dimensions over local homomorphisms
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