Diversity in interaction strength promotes rich dynamical behaviours in a three-species ecological system

Abstract Asymmetrical interactions are thought to have an important influence on multi-species competitive systems, and understanding this ecological process is a challenging task because of uncertain roles that asymmetrical interactions can have in maintaining species biodiversity. To address this problem, we employ a simple ecological model for multiple species with asymmetrical competitive strength and we analyse this model using the techniques from dynamical systems and bifurcation analysis. In particular, we examine the stability properties of steady states and also its bifurcation structures under parameter variation. We demonstrate that there exists threshold values for asymmetrical competitive strength, which correspond to transcritical and supercritical Hopf bifurcations. The occurrence of these bifurcations give rise to numerous dynamics in the model e.g. multi-species coexistence, species exclusion, alternative stable state communities and oscillatory dynamics among multiple species. Additionally, we observe the conditions under which co-dimension two (Gavrilov-Guckenheimer) bifurcation occurs as a result of the interaction between transcritical and Hopf bifurcations, which can lead to complex dynamics. We also investigate how diversity in interaction strength between multiple competing species causes counterintuitive observations: on one hand, asymmetrical interactions promote the maintenance of biodiversity through multi-species coexistence state and also coexistence via stable limit cycles (corresponding to oscillatory dynamics); on the other hand, we also observe that the occurrence of stable limit cycles can lead to destabilisation of multi-species communities.

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