Predicting attenuant and resonant 2-cycles in periodically forced discrete-time two-species population models

Figures & data

Table 1. Examples of multiparameter population models.

Model number	Model, F(P(x, y))=	References
I		Logistic model 20
II		Ricker 21
III		Beverton–Holt (B, C>1) 1
IV		Hassell 13

Table 2. Stability conditions for the six-parameter two-species models given in Table 1.

	Parameters giving stable carrying capacity, note with
Model number	B, C>1 in Model III
I	4ST>BLT+CMS, LT+MS>ST,
II	4ST>BLT+CMS, LT+MS>ST,
III	, LT+MS>ST,
IV	, LT+MS>ST,

Figure 1. Regions of attenuance and resonance in the a, b, and C plane for the 2-periodic Logistic model when γ=0 and L=3T/4.

Figure 2. Regions of attenuance and resonance in the a, b, and C plane for the 2-periodic Ricker model for γ=0 and L=3T/4.

Figure 3. Regions of attenuance and resonance in the a, b, and C plane for the 2-periodic Beverton–Holt model with γ=0 and L=3T/4.

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Beverton , R. and Holt , S. 1957 . On the dynamics of exploited fish populations . Fishery Investig. , 19 : 533

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