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A two species commensal symbiosis model with Holling type functional response and density dependent birth rate takes the form (Formula presented) is proposed and studied in this paper. For autonomous case, i.e., aij, bi, i = 1, 2, j = 1, 2, 3, 4 p and c1 are all positive constants, p ≥ 1, sufficient conditions which ensure the local and global stability of the boundary equilibrium and positive equilibrium are obtained, respectively; For non-autonomous case, i.e., aij, bi and c1 are all continuous functions bounded above and below by positive constans, p ≥ 1 is a positive constant, sufficient conditions which ensure the permanence and partial survival of the system are obtained, respectively. Sufficient conditions-p which ensure the existence of at least one positive T-periodic solution is obtained. Our study shows that the birth rate of species and the commensal intensity between the species play important role on the dynamic behaviors of the system. © 2019, International Association of Engineers. All rights reserved.
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Engineering Letters
ISSN: 1816-093X
Year: 2019
Issue: 2
Volume: 27
Page: 295-302
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