, Volume 12, Issue 2, pp 305-314

An Index Theory for Positive Dynamical Systems with an Application to Lotka–Voterra Systems

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Abstract

In this paper we develop an index theory of positive dynamical systems in planar case. We present a formula of index sum of isolated zeros a positive dynamical system on the positive orthant of R 2. As an application, we present some sufficient conditions on existence of zeros of Lotka–Voterra systems in the positive orthant of R 2.