Jason Matthiopoulos, John M. Halley, and Robert Moss. 2005. Socially induced Red Grouse population cycles need abrupt transitions between tolerance and aggression. Ecology 86:1883–1893.

Appendices

Appendix A: Local stability analysis of the general model equation (Eq. 11).
Ecological Archives E086-099-A1.

Appendix B: Application of stability conditions in Eq. 14 to specific examples.
Ecological Archives E086-099-A2.

Appendix C: Perturbation analysis of the necessary and sufficient conditions for cycles.
Ecological Archives E086-099-A3.

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