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The global stability of coexisting equilibria for three models of mutualism

Paul Georgescu Hong Zhang Daniel Maxin

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MBE2016,1,101doi:10.3934/mbe.2016.13.101

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.

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