# American Institute of Mathematical Sciences

2016, 13(1): 101-118. doi: 10.3934/mbe.2016.13.101

## The global stability of coexisting equilibria for three models of mutualism

 1 Department of Mathematics, Technical University of Iaşi, Bd. Copou 11, 700506 Iaşi, Romania 2 Department of Financial Mathematics, Jiangsu University, ZhenJiang, Jiangsu, 212013, China, China

Received  January 2015 Revised  June 2015 Published  October 2015

We analyze the dynamics of three models of mutualism, establishing the global stability of coexisting equilibria by means of Lyapunov's second method. This further establishes the usefulness of certain Lyapunov functionals of an abstract nature introduced in an earlier paper. As a consequence, it is seen that the use of higher order self-limiting terms cures the shortcomings of Lotka-Volterra mutualisms, preventing unbounded growth and promoting global stability.
Citation: Paul Georgescu, Hong Zhang, Daniel Maxin. The global stability of coexisting equilibria for three models of mutualism. Mathematical Biosciences & Engineering, 2016, 13 (1) : 101-118. doi: 10.3934/mbe.2016.13.101
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