9. Pulse and Recycle (PULSE)

This Pulse model is a production-consumption model with recycling feedback. It is more realistic for producer-consumer systems than the prey-predator model (Models #6). An example is grassland with grasshoppers that have a slow consumption mode and a frenzied consumption mode. For several seasons the quantity of grasshoppers increases slowly, eating only a small portion of accumulating grasses. When there is enough accumulated vegetation for the grasshoppers to have a surge of reproduction and rapid consumption they eat the grass to a low level. (Figure III-10).

The model has two modes of consumption, the slow gradual one and the epidemic destructive one. This pulsing sequence may be the most characteristic pattern in many ecosystems, economic systems and others. Growth of any system may reach a level that leads to a pulse of consumption, followed by a repetition.

In this model recycling of outputs of consumption (wastes) are used by production. Materials are conserved in the system: total materials (TM) include those available for production (M), those incorporated in the producers (FI*Q) and those in the consumers (F2*C). The linear pathway of slow consumption is proportional to the quantity of producers (KI*E*Q).

The rapid consumption pathway is caused by a super­-accelerated growth of consumers. Mathematically, this is quadratic auto-catalytic (K3*Q*C*C), which represents processes that go faster due to self-interactions. (See Part II.8, Super-accelerated Growth).

The surge of consumption is initiated automatically without switches when the mathematical term for the feedback consumer pathway (K3*Q*C*C) exceeds the term for consumer recycling and depreciation (K4*C). The programs are in Table III-10. In this program scaling factors are divided (Q/Q0) rather than multiplied (Q*Q0).

Examples of Pulse and Recycle Models

In rainforest areas like the Amazon River basin, tribal people practice "slash and burn" shifting agriculture. Trees were cut and burned, the area was planted and harvested for several years; and then it was abandoned to regrow when the people moved to fresh site. Later, in a hundred years or so, after the trees had regrown, the process was repeated.

The world follows a pulsing pattern. As fossil fuels were built-up by geological process, occasional fires used them slowly. When the accumulation was enough, humans came along to build a civilization that is consuming them rapidly. When we have used them up how long will it take for enough to be produced to support another civilization - 2 million years?

This model represents predator-prey systems like the snowshoe hare and the lynx. It takes a big population of hares before the lynx come to eat them. After the lynx consume the hares' down to very few, the hare population has to have time to build up again.

An economic example is the inventory cycle of selling of goods in a store. Sales go steadily, but when enough of the goods accumulate, they are put on sale and more of them sell quickly. This pulsing often occurs in three-year intervals.

"What if" Experimental Problems

  1. If fertilizer were added to the shifting agriculture farms in the rain forest, what would that do to the pulsing of the system? Make TM 300 to increase the total nutrients, and run the program again.

  2. In the inventory example, what would happen to the time of special sales of blankets if the regular sales of the blankets increased? What are the coefficients, which represent regular sales? Double K2 and K5 and run the program again. Notice how often it pulses and how high the inventory goes before a sale is necessary. Double K2 and K5 again and run it.

  3. What would happen to the pulsing of the geological cycle if people programmed themselves to use just the amount of fuels that was being made? To make fuels used equal to fuels made, replace K5*Q in statement 220 with K1*E*M.


Howard T. Odum* and Elisabeth C. Odum+
* Dept. of Environmental Engineering Sciences, UF
+ Santa Fe Community College, Gainesville

Center for Environmental Policy, 424 Black Hall
University of Florida, Gainesville, FL, 32611
Copyright 1994

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