Mathematica code to calculate the overcompensation and consumerresource stability boundaries of the semi-discrete model.
Ecological Archives E089-017-S1.
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Department of Ecology, Evolution and Marine Biology
University of California Santa Barbara, CA 93106
StabilityAnalysisSemi-DiscreteLogistic.nb - Mathematica code
StabilityAnalysisSemi-DiscreteLogistic.pdf - PDF of the code
Mathematica (version 5) code to calculate the overcompensation and consumer-resource stability boundaries of the semi-discrete model as a function of mu and alpha, for different values of rho. The analysis is decsribed in Appendix A. The code calculates the stability boundaries in sections.
data1 - bottom part of the consumer-resource boundary (heavy solid line in Fig. 2a of the main text);
data2 - top part of the consumer-resource boundary (dotted line in Fig. 2a);
data3 - top of the left arm of the overcompensation boundary (dashed line in Fig. 2a) until it crosses the consumer-resource boundary;
data4 - bottom of the left arm of the overcompensation boundary (dashed line in Fig. 2a) until the minimum of the boundary;
data5 - right arm of the overcompensation boundary (dashed line in Fig. 2a).
Some parameter definitions:
J11, J12, J21, J22 - elements of the Jacobian from the linear stability analysis of the model.
Cond1 - condition for existence of a positive equilibrium;
Cond2 - transition from stability to overcompensation cycles;
Cond3 - transition from stability to consumer - resource cycles;
Period - period of population cycles on the consumer - resource stability boundary (for a discussion of caclulating boundary conditions and the period see Gurney, W. S. C., and R. M. Nisbet. 1998. Ecological Dynamics. Oxford University Press, New York, New York, USA)
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