I have tried exploring different periodic functions combined with exponential growth rates, however, all my models fail to overshoot the carrying capacity. I have also examined piece-wise functions that could work, however something that is more elegant would be much more pleasing.
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Are you looking for an ODE ? What are your trials ? You need to provide more details. – nicomezi May 10 '23 at 06:09
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Yes an ODE, my trials are: dN/dt=rN (1-N/(a sinb(t+c)+d)) dN/dt = rN(1-N/K) - cK – Armaan Hooda May 10 '23 at 06:12
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Because of the Lipschitz theorem, I think you have to consider second order equations at least. Because the carrying capacity should be an equilibrium state, doesn't it ? – nicomezi May 10 '23 at 06:14
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That's exactly my intention: exploring varrying carrying capacities with boom and bust cycles – Armaan Hooda May 10 '23 at 06:18