# Phase switching in population cycles

##### Citations

11 citations

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^{1}, Cornell University

^{2}, College of William & Mary

^{3}, University of Arizona

^{4}

5 citations

### Cites background from "Phase switching in population cycle..."

...Noise, always present in population dynamics, causes cycle irregularities such as outbreaks, switches in oscillation phase [28], and episodes of damped oscillations caused by “saddle fly-bys” [11] or other stochastic visitations of unstable equilibria....

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...The discrete stage-structured “LPA” Tribolium model has successfully explained and predicted nonlinear phenomena in a variety of contexts, including transitions between dynamic regimes (such as equilibria, 2-cycles, 3-cycles, invariant loops, and chaos), multiple attractors, saddle influences, stable and unstable manifolds, and lattice effects [4, 7, 5, 10, 8, 11, 12, 9, 13, 14, 15, 17, 18, 28, 24, 27, 25, 26, 30]....

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4 citations

##### References

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### "Phase switching in population cycle..." refers methods in this paper

...The idea is to look at the population at every other time-step by constructing the so-called c̀omposite' map (e.g. see May & Oster 1976)....

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599 citations

### "Phase switching in population cycle..." refers background or methods in this paper

...…including the transitions between dynamic regimes (such as equilibria, two-cycles, three-cycles, invariant loops, and chaos), multiple attractors, and saddle in£uences (Costantino et al. 1995, 1997, 1998; Cushing 1996, 1998; Dennis et al. 1995, 1997; Desharnais et al. 1997; Henson et al. 1999)....

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...Local stability results for both the LPA model and its composite are obtained using standard linearization techniques (Cushing 1998; Guckenheimer & Holmes 1983)....

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...Local stability results for both the LPA model and its composite are obtained using standard linearization techniques (Cushing1998; Guckenheimer & Holmes1983)....

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...it is a saddle point; see Cushing et al. (1998))....

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