One of the most interesting dynamics between populations has to do with interactions between species, such as the interaction of a predator species and its food species, its prey. The American biophysicist Alfred Lotka and the Italian mathematician Vito Volterra were the first (in 1925) to propose a model for interactions between predator and prey; their model is called the Lotka-Volterra model. Anand Sarwate, who blogs at An Ergodic Walk, points to an empirically interesting economic application (think government and taxpayer) based on the Lotka-Volterra system:
CYCLES OF FEAR: PERIODIC BLOODSUCKING RATES FOR VAMPIRES
R. F. Hartl, A. Mehlmann, and A. Novak, Journal of Optimization Theory and Applications, Vol.75 No. 3, 1992
Abstract: In this paper, we present a new approach for modeling the dynamic intertemporal confrontation between vampires and humans. It is assumed that the change of the vampiristic consumption rate induces costs and that the vampire community also derives some utility from possessing humans and not only from consuming them. Using the Hopf bifurcation theorem it can be shown that cyclical bloodsucking strategies are optimal. These results are in accordance with empirical evidence.
This paper analyzes a mathematical model of bloodsucking rates for vampires using control theory. However, as they note in the introduction,
"To a traditional vampirologist, the use of optimal control theory against vampires, as exercised in Ref. 6, seems highly questionable. This is due to the fact that the application of Pontryagin’s principle requires the derivation of a shadow price for vampires. Such a price is, however, nonexistent since vampires do not have a shadow."
As a predator-prey scenario, we can model the dynamics of the population using some differential equations. The problem for the vampires is to set a bloodsucking rate (humans per vampire) so as to maximize a utility function subject to the dynamics. However, the model has to be made more sophisticated to account for the cyclical bloodsucking patterns found in real vampires. The modifications are twofold — firstly, vampires also derive some utility from posessing humans rather than just sucking blood from them, and secondly, changing the consumption rate penalizes the utility. So in this push-and-pull framework they can derive some cycles, appropriately named “cycles of fear” in which the bloodsucking rate is modulated over time to achieve a stable tradeoff and net utility.
The full version, which is not to be missed, can be found via SpringerLink. For some earlier comments on the optimal destruction of vampires and macroeconomic policy (which involves the shadow price), see this related JSTOR article.
CYCLES OF FEAR: PERIODIC BLOODSUCKING RATES FOR VAMPIRESR. F. Hartl, A. Mehlmann, and A. Novak, Journal of Optimization Theory and Applications, Vol.75 No. 3, 1992
Abstract: In this paper, we present a new approach for modeling the dynamic intertemporal confrontation between vampires and humans. It is assumed that the change of the vampiristic consumption rate induces costs and that the vampire community also derives some utility from possessing humans and not only from consuming them. Using the Hopf bifurcation theorem it can be shown that cyclical bloodsucking strategies are optimal. These results are in accordance with empirical evidence.
This paper analyzes a mathematical model of bloodsucking rates for vampires using control theory. However, as they note in the introduction,
"To a traditional vampirologist, the use of optimal control theory against vampires, as exercised in Ref. 6, seems highly questionable. This is due to the fact that the application of Pontryagin’s principle requires the derivation of a shadow price for vampires. Such a price is, however, nonexistent since vampires do not have a shadow."
As a predator-prey scenario, we can model the dynamics of the population using some differential equations. The problem for the vampires is to set a bloodsucking rate (humans per vampire) so as to maximize a utility function subject to the dynamics. However, the model has to be made more sophisticated to account for the cyclical bloodsucking patterns found in real vampires. The modifications are twofold — firstly, vampires also derive some utility from posessing humans rather than just sucking blood from them, and secondly, changing the consumption rate penalizes the utility. So in this push-and-pull framework they can derive some cycles, appropriately named “cycles of fear” in which the bloodsucking rate is modulated over time to achieve a stable tradeoff and net utility.
The full version, which is not to be missed, can be found via SpringerLink. For some earlier comments on the optimal destruction of vampires and macroeconomic policy (which involves the shadow price), see this related JSTOR article.
Mahalanobis - am 2006-10-24 21:16
Hedgehog (guest) meinte am 26. Oct, 09:00:
"an empirically interesting economic application (think government and taxpayer)"
I wonder, though, in the context of your taxpayer vs. government interpretation, what is the interpretation of "stakes"? Is it some kind of campaign money in support of neocon candidates promising to "starve the beast"? It sounds a bit strained, although it's probably just my lack of imagination.I think the more appropriate interpretation of the JPE 1982 article is the war on terrorism where the "stakes" are the weapons used to "neutralize" terrorists ("vampires").
Mariny (guest) meinte am 28. Oct, 11:24:
I know that some epochs later, the blood was a medicine, which cured from almost all diseases. The blood should be taken just from babies, as their blood is the most pure and effective.It was taken from animals too, however childish(human)blood was much more appreciated.
