User:Carl Boettiger/Notebook/Stochastic Population Dynamics/2010/05/26
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Rethinking Beetles Noise
and the larval fluctuations are essentially:
where βi is the intrinsic noise of the age class. Hence a class i which propagates large noise to another class j has a large . If this term is a linear transition λXi, then the same term appears in fi and hence damps the noise and cancels out. Hence noise must propagate into a class through nonlinear transition rates OR through an asymmetry in the transition (i.e. the c_1, c_2 large noise example in the generalized crowley).
Adding age delay to beetle dynamics
Current formulation has used exponential waiting times between stages. By subdividing the classes (increasing the system dimension size) and creating single jump within-state transitions, these become gamma-distributed waiting times. Adding ten steps to each phase and a little parameter fiddling introduces sustained oscillations. (Version-stable code).
Xo = 100
and now we have noise in oscillatory, gamma-waiting model:
Misc / Code notes