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Identifying early warning signs of sudden population changes and mechanismsleading to regime shifts are highly desirable in population biology. In thispaper, a two-trophic ecosystem comprising of two species of predators,competing for their common prey, with explicit interference competition isconsidered. With proper rescaling, the model is portrayed as a singularlyperturbed system with fast prey dynamics and slow dynamics of the predators. Ina parameter regime near singular Hopf bifurcation, chaotic mixed-modeoscillations (MMOs), featuring concatenation of small and large amplitudeoscillations are observed as long-lasting transients before the systemapproaches its asymptotic state. To analyze the dynamical cause that initiatesa large amplitude oscillation in an MMO orbit, the model is reduced to asuitable normal form near the singular-Hopf point. The normal form possesses aseparatrix surface that separates two different types of oscillations. A largeamplitude oscillation is initiated if a trajectory moves from the "inner" tothe "outer side" of this surface. A set of conditions on the normal formvariables are obtained to determine whether a trajectory would exhibit anothercycle of MMO dynamics before experiencing a regime shift (i.e. approaching itsasymptotic state). These conditions can serve as early warning signs for asudden population shift in an ecosystem.

Analysis of long-term transients and detection of early warning signs of major population changes in a two-timescale ecosystem