In this paper, we propose a stochastic service-resource mutualism model with Lévy noises and harvesting. Under some assumptions, we study several dynamical properties of the model. We first obtain the thresholds between persistence and extinction for both the service species and the resource species. Then we give sharp sufficient conditions for stability in distribution of the model. Finally, we establish sufficient and necessary criteria for the existence of the optimal harvesting policy. The optimal harvesting effort and maximum of sustainable yield are also obtained. Our results reveal that the persistence, extinction, stability in distribution and optimal harvesting strategy have close relationships with the random noises.
Keywords: Service-resource mutualism model, white noise, Lévy jumps, persistence, optimal harvesting
Wang, Hui 1 ; Du, Chenxi 1 ; Liu, Meng 2
@article{10_22436_jnsa_010_12_07,
author = {Wang, Hui and Du, Chenxi and Liu, Meng },
title = {Dynamics of a stochastic service-resource mutualism model with {L\'evy} noises and harvesting},
journal = {Journal of nonlinear sciences and its applications},
pages = {6205-6218},
year = {2017},
volume = {10},
number = {12},
doi = {10.22436/jnsa.010.12.07},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.12.07/}
}
TY - JOUR AU - Wang, Hui AU - Du, Chenxi AU - Liu, Meng TI - Dynamics of a stochastic service-resource mutualism model with Lévy noises and harvesting JO - Journal of nonlinear sciences and its applications PY - 2017 SP - 6205 EP - 6218 VL - 10 IS - 12 UR - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.12.07/ DO - 10.22436/jnsa.010.12.07 LA - en ID - 10_22436_jnsa_010_12_07 ER -
%0 Journal Article %A Wang, Hui %A Du, Chenxi %A Liu, Meng %T Dynamics of a stochastic service-resource mutualism model with Lévy noises and harvesting %J Journal of nonlinear sciences and its applications %D 2017 %P 6205-6218 %V 10 %N 12 %U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.12.07/ %R 10.22436/jnsa.010.12.07 %G en %F 10_22436_jnsa_010_12_07
Wang, Hui ; Du, Chenxi ; Liu, Meng . Dynamics of a stochastic service-resource mutualism model with Lévy noises and harvesting. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 12, p. 6205-6218. doi: 10.22436/jnsa.010.12.07
[1] Multiplicity of solutions for a class of non-local elliptic operators systems, Bull. Korean Math. Soc., Volume 54 (2017), pp. 715-729 | DOI | Zbl
[2] Stochastic population dynamics driven by Lévy noise, J. Math. Anal. Appl., Volume 391 (2012), pp. 363-375 | DOI
[3] Systémes d’équations différentielles d’oscillations non linéaires, (French) Rev. Math. Pures Appl., Volume 4 (1959), pp. 267-270 | Zbl
[4] Nonlinear programming , Theory and algorithms, John Wiley & Sons, New York- Chichester-Brisbane, 1979
[5] Harvesting natural populations in a randomly fluctuating environment, Science, Volume 197 (1977), pp. 463-465 | DOI
[6] Ecology, Individuals, populations and communities, Blackwell scientific publications, Cambridge, 1986
[7] Variable effort harvesting models in random environments: generalization to density-dependent noise intensities, Deterministic and stochastic modeling of biointeraction, West Lafayette, IN, (2000), Math. Biosci., Volume 177/178 (2002), pp. 229-245 | Zbl | DOI
[8] Optimal harvesting of diffusive models in a nonhomogeneous environment , Nonlinear Anal., Volume 71 (2009), pp. 1-2173 | DOI | Zbl
[9] Continuous versus pulse harvesting for population models in constant and variable environment, J. Math. Biol., Volume 57 (2008), pp. 413-434 | DOI | Zbl
[10] Mathematical bioeconomics, The optimal management of renewable resources, Second edition, With a contribution by Gordon Munro, Pure and Applied Mathematics (New York), A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1990
[11] Ergodicity for infinite-dimensional systems, London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 1996 | DOI
[12] Optimal harvesting policy for single population with periodic coefficients, Math. Biosci., Volume 152 (1998), pp. 165-177 | Zbl | DOI
[13] Stability for multispecies population models in random environments, Nonlinear Anal., Volume 10 (1986), pp. 1411-1419 | Zbl | DOI
[14] Modelling and analysis of a harvested prey-predator system incorporating a prey refuge, J. Comput. Appl. Math., Volume 185 (2006), pp. 19-33 | Zbl | DOI
[15] Itô ’s stochastic calculus: its surprising power for applications, Stochastic Process. Appl., Volume 120 (2010), pp. 622-652 | DOI | Zbl
[16] Optimal harvesting of a stochastic logistic model with time delay, J. Nonlinear Sci., Volume 25 (2015), pp. 277-289 | Zbl | DOI
[17] Analysis of a stochastic tri-trophic food-chain model with harvesting, J. Math. Biol., Volume 73 (2016), pp. 597-625 | DOI | Zbl
[18] Dynamics of a stochastic one-prey two-predator model with Lévy jumps, Appl. Math. Comput., Volume 284 (2016), pp. 308-321 | DOI
[19] Optimal harvesting of a stochastic delay competitive model, Discrete Contin. Dyn. Syst. Ser. B, Volume 22 (2017), pp. 1493-1508 | DOI | Zbl
[20] Dynamics of a stochastic regime-switching predator-prey model with harvesting and distributed delays, Nonlinear Anal. Hybrid Syst., Volume 28 (2018), pp. 87-104 | DOI | Zbl
[21] Optimal control strategy for an impulsive stochastic competition system with time delays and jumps, Phys. A, Volume 477 (2017), pp. 99-113 | DOI
[22] Stochastic Lotka-Volterra systems with Lévy noise, J. Math. Anal. Appl., Volume 410 (2014), pp. 750-763 | Zbl | DOI
[23] Stochastic differential equations with Markovian switching, Imperial College Press, London, 2006
[24] Consumer-resource dynamics, Princeton University Press, Princeton, 2003
[25] Uni-directional consumer-resource theory characterizing transitions of interaction outcomes, Ecol. Complex., Volume 8 (2011), pp. 249-257 | DOI
[26] Optimal harvesting policy of a stochastic two-species competitive model with Lévy noise in a polluted environment, Phys. A, Volume 477 (2017), pp. 20-33 | DOI
[27] Permanence and extinction in a stochastic service-resource mutualism model, Appl. Math. Lett., Volume 69 (2017), pp. 1-7 | DOI | Zbl
[28] On hybrid competitive Lotka-Volterra ecosystems, Nonlinear Anal., Volume 71 (2009), pp. 1-1370 | Zbl | DOI
[29] Ergodic method on optimal harvesting for a stochastic Gompertz-type diffusion process, Appl. Math. Lett., Volume 26 (2013), pp. 170-174 | DOI | Zbl
[30] Optimal harvesting for a logistic population dynamics driven by a Lévy process, J. Optim. Theory. Appl., Volume 161 (2014), pp. 969-979 | Zbl | DOI
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