Symposium: Insect Behavioral Ecology--'89: Chaos and Phase-Locking in Predator-Prey Models in Relation to the Functional Response

Allen, J. C.

Abstract


The dynamics of a simple predator-prey model: @? = @f x(1-x)-@c g(x)z (prey) @? = (x-y)/@t (lagged prey) @? = @cg(y)z- @uz (predator) with periodic forcing (@f) on the prey's reproductive rate and a functional response, g(x), is investigated in relation to parameters and the functional response. The system is sampled at the forcing period and plotted against a parameter for each of four functional responses: Linear, Type 1, Type 2 and Type 3. Sampling at the forcing period allows one to see when the system is phase-locked in some ratio with the forcing cycle. The analysis reveals very complicated and unexpected switching between different phase-locking ratios alternating with regions of quasiperiodic and chaotic behavior within each functional response as a parameter is varied. Of the four functional responses tested, the Type 2 response produces the most complex behavior.

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