Persistence and extinction in a stochastic nonautonomous logistic model of population dynamics
Authors:
O. D. Borysenko and D. O. Borysenko
Translated by:
N. N. Semenov
Journal:
Theor. Probability and Math. Statist. 99 (2019), 67-75
MSC (2010):
Primary 60H10; Secondary 60J75, 60G51, 92D25
DOI:
https://doi.org/10.1090/tpms/1080
Published electronically:
February 27, 2020
MathSciNet review:
3908656
Full-text PDF
Abstract |
References |
Similar Articles |
Additional Information
Abstract: The nonautonomous logistic differential equation is studied for the case where the rate of the population growth coefficient is perturbed by a white noise or by a centered or noncentered Poisson noise. Sufficient conditions are obtained for the almost sure population extinction, nonpersistence of the population in the mean, weak persistence of the population in the mean, and strong persistence of the population in the mean.
References
- Mimmo Iannelli and Andrea Pugliese, An introduction to mathematical population dynamics, Unitext, vol. 79, Springer, Cham, 2014. Along the trail of Volterra and Lotka; La Matematica per il 3+2. MR 3288300
- K. Gopalsamy, Stability and oscillations in delay differential equations of population dynamics, Mathematics and its Applications, vol. 74, Kluwer Academic Publishers Group, Dordrecht, 1992. MR 1163190
- Meng Liu and Ke Wang, Persistence and extinction in stochastic non-autonomous logistic systems, J. Math. Anal. Appl. 375 (2011), no. 2, 443–457. MR 2735535, DOI https://doi.org/10.1016/j.jmaa.2010.09.058
- Jianhai Bao and Chenggui Yuan, Stochastic population dynamics driven by Lévy noise, J. Math. Anal. Appl. 391 (2012), no. 2, 363–375. MR 2903137, DOI https://doi.org/10.1016/j.jmaa.2012.02.043
- Sheng Wang, Linshan Wang, and Tengda Wei, A note on a competitive Lotka-Volterra model with Lévy noise, Filomat 31 (2017), no. 12, 3741–3748. MR 3703869, DOI https://doi.org/10.2298/fil1712741w
- O. D. Borysenko and D. O. Borysenko, Non-autonomous stochastic logistic differential equation with non-centered Poisson measure, Bull. Taras Shevchenko Nat. Kyiv Univ., Series: Physics & Mathematics (2017), no. 4, 9–14.
- I. I. Gikhman and A. V. Skorokhod, Stokhasticheskie differentsial′nye uravneniya i ikh prilozheniya, “Naukova Dumka”, Kiev, 1982 (Russian). MR 678374
- R. Sh. Liptser and A. N. Shiryaev, Teoriya martingalov, Teoriya Veroyatnosteĭ i Matematicheskaya Statistika. [Probability Theory and Mathematical Statistics], “Nauka”, Moscow, 1986 (Russian). MR 886678
References
- M. Iannelli and A. Pugliese, An Introduction to Mathematical Population Dynamics, Springer, 2014. MR 3288300
- K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer Academic, Dordrecht, 1992. MR 1163190
- Meng Liu and Ke Wanga, Persistence and extinction in stochastic non-autonomous logistic systems, J. Math. Anal. Appl. 375 (2011), 443–457. MR 2735535
- J. Bao and Ch. Yuan, Stochastic population dynamics driven by Lévy noise, J. Math. Anal. Appl. 391 (2012), 363–375. MR 2903137
- S. Wang, L. Wang, and T. Wei, A note on a competitive Lotka–Volterra model with Lévy noise, Filomat 31 (2017), no. 12, 3741–3748. MR 3703869
- O. D. Borysenko and D. O. Borysenko, Non-autonomous stochastic logistic differential equation with non-centered Poisson measure, Bull. Taras Shevchenko Nat. Kyiv Univ., Series: Physics & Mathematics (2017), no. 4, 9–14.
- I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations and their Applications, “Naukova Dumka”, Kiev, 1982. (Russian) MR 678374
- R. Sh. Liptser and A. N. Shiryayev, Theory of Martingales, “Nauka”, Moscow, 1986. (Russian) MR 886678
Similar Articles
Retrieve articles in Theory of Probability and Mathematical Statistics
with MSC (2010):
60H10,
60J75,
60G51,
92D25
Retrieve articles in all journals
with MSC (2010):
60H10,
60J75,
60G51,
92D25
Additional Information
O. D. Borysenko
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email:
odb@univ.kiev.ua
D. O. Borysenko
Affiliation:
Department of Integral and Differential Equations, Faculty for Mechanics and Mathematics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email:
dima.borisenko.wrk@gmail.com
Keywords:
Nonautonomous logistic stochastic differential equation,
centered and noncentered Poisson noise,
extinction,
nonpersistence in the mean,
weak persistence in the mean,
strong persistence in the mean
Received by editor(s):
August 20, 2018
Published electronically:
February 27, 2020
Article copyright:
© Copyright 2020
American Mathematical Society
