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A Note on Stability of Stochastic Logistic Model by Incorporating the Ornstein-Uhlenbeck Process

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  • Tawfiqullah Ayoubi
  • Abdul Munir Khirzada

Abstract

In this research, we first prove that the stochastic logistic model (10) has a positive global solution. Subsequently, we introduce the sufficient conditions for the stochastically stability of the general form of stochastic differential equations (SDEs) in terms of equation (1), for zero solution by using the Lyapunov function. This result is verified via several examples in Appendix A. Besides; we prove that the stochastic logistic model, by incorporating the Ornstein-Uhlenbeck process is stable in zero solution. Furthermore, the simulated results are displayed via the 4-stage stochastic Runge-Kutta (SRK4) numerical method.

Suggested Citation

  • Tawfiqullah Ayoubi & Abdul Munir Khirzada, 2020. "A Note on Stability of Stochastic Logistic Model by Incorporating the Ornstein-Uhlenbeck Process," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 12(2), pages 1-52, April.
    • Handle: RePEc:ibn:jmrjnl:v:12:y:2020:i:2:p:52
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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