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We propose a two-species commensal symbiosis model with ratio-dependent functional response dx dt = x ( − a1 − b1x+ c1y x+ y ) , dy dt = y(a2 − b2y). For autonomous case, we show that the unique positive equilibrium is globally stable if a1 < c1 holds, and the boundary equilibrium (0, a2 b2 ) is globally stable if a1 > c1 holds. For nonautonomous case, some sufficient conditions which ensure the permanence and global attractivity of the system are obtained. Numeric simulations are carried out to show the feasibility of the main results. c ©2016 All rights reserved.

Dynamic behaviors of a commensal symbiosis model with ratio-dependent functional response and one party can not survive independently