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Ecological resilience refers to the ability of a system to retain its statewhen subject to state variables perturbations or parameter changes. Whileunderstanding and quantifying resilience is crucial to anticipate the possibleregime shifts, characterizing the influence of the system parameters onresilience is the first step towards controlling the system to avoidundesirable critical transitions. In this paper, we apply tools of qualitativetheory of differential equations to study the resilience of competingpopulations as modeled by the classical Lotka-Volterra system. Within the highinterspecific competition regime, such model exhibits bistability, and theboundary between the basins of attraction corresponding to exclusive survivalof each population is the stable manifold of a saddle-point. Studying suchmanifold and its behavior in terms of the model parameters, we characterizedthe populations resilience: while increasing competitiveness leads to higherresilience, it is not always the case with respect to reproduction. Within apioneering context where both populations initiate with few individuals,increasing reproduction leads to an increase in resilience; however, within anenvironment previously dominated by one population and then invaded by theother, an increase in resilience is obtained by decreasing the reproductionrate. Besides providing interesting insights for the dynamics of competingpopulation, this work brings near to each other the theoretical concepts ofecological resilience and the mathematical methods of differential equationsand stimulates the development and application of new mathematical tools forecological resilience.

Resilience Analysis for Competing Populations