Stability of three species symbiosis model with delay and stochastic perturbations. (English) Zbl 1496.92079
Summary: In this paper a three-species symbiosis population model with delay and stochastic perturbations is considered. The model is modified by considering more general rate which ensure the existence of at least one nontrivial equilibrium. Conditions for the existence of positive equilibrium of the considered model are obtained. New sufficient conditions of stability in probability for the obtained positive equilibrium are formulated in the terms of linear matrix inequalities (LMIs), which can be investigated by virtue of MATLAB. Besides some necessary stability conditions are formulated in the form of simple analytical inequalities. The results obtained are illustrated via numerical simulations of a solution of the considered model.
MSC:
| 92D25 | Population dynamics (general) |
| 34D10 | Perturbations of ordinary differential equations |
| 34D20 | Stability of solutions to ordinary differential equations |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
stochastic differential equations; positive equilibrium; stability in probability; asymptotic mean square stability; linear matrix inequalities (LMIs)Software:
MatlabReferences:
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