A stochastic mussel-algae model under regime switching
Open Access
- 1 January 2022
- journal article
- research article
- Published by American Institute of Mathematical Sciences (AIMS) in Mathematical Biosciences and Engineering
- Vol. 19 (5), 4794-4811
- https://doi.org/10.3934/mbe.2022224
Abstract
We investigate a novel model of coupled stochastic differential equations modeling the interaction of mussel and algae in a random environment, in which combined effect of white noises and telegraph noises formulated under regime switching are incorporated. We derive sufficient condition of extinction for mussel species. Then with the help of stochastic Lyapunov functions, a well-grounded understanding of the existence of ergodic stationary distribution is obtained. Meticulous numerical examples are also employed to visualize our theoretical results in detail. Our analytical results indicate that dynamic behaviors of the stochastic mussel-algae model are intimately associated with two kinds of random perturbations.Keywords
This publication has 44 references indexed in Scilit:
- The ergodic property and positive recurrence of a multi-group Lotka–Volterra mutualistic system with regime switchingSystems & Control Letters, 2013
- Asymptotic behaviour of the stochastic Lotka–Volterra modelJournal of Mathematical Analysis and Applications, 2003
- Investigation of the effects of current velocity on mussel feeding and mussel bed stability using an annular flumeHelgoland Marine Research, 2002
- Algal concentration profiles above mussel bedsJournal of Sea Research, 2000
- Potential Abiotic and Biotic Impacts of Zebra Mussels on the Inland Waters of North AmericaAmerican Zoologist, 1996
- Potential effects of global warming on northern European freshwater fish and fisheriesFisheries Management and Ecology, 1996
- Temporal and spatial patterns of growth in mussels Mytilus edulis on an offshore platform: relationships to water temperature and food availabilityJournal of Experimental Marine Biology and Ecology, 1987
- Importance to Mussels of the Benthic Boundary LayerCanadian Journal of Fisheries and Aquatic Sciences, 1984
- The Influence of External Real and White Noise on the LOTKA‐VOLTERRA ModelBiometrical Journal, 1979
- The Dynamics of a Population in a Markovian EnvironmentEcology, 1978