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1. Introduction
Typically, systems exhibit both positive and negative feedback processes
that have different and varying strengths. Predator-prey relations are a case
in point. The increase in prey population will mean a tendency to produce
even more prey . This is a positive feedback. Similarly, an increase in the
number of predators means that more predators can be born . The negative
feedback is present in the interaction between the two populations, and the
strength of this feedback depends on what happens with each of the two
populations. One possible outcome is a continuous fluctuation in both
populations, which neither settle down to a long-term steady-state, nor result in explosive dynamics.
Variation in the strength of feedback processes are often reflected in
nonlinear relations among system components. Such nonlinear relations
are present if a control variable does not depend on other variables in a linear fashion , but changes, for example, with the square of some other variable. As a result of nonlinear feedback processes, systems may exhibit complex dynamic behavior.
Another source for changes in the strength of a feedback through time
are the delays by which one component changes in response to changes
in another component. In some cases, the length of the time lag is rather
well known. For example, an increase in horseshoe crab populations
means an increased number of eggs being laid in a bay, and thus greater
food supply for sea birds. An increase in food supply translates fairly
quickly into higher body mass of the birds , but also has time-delayed effects on the population dynamics of birds. Well-fed birds are more likely
to survive migration and are more likely to successfully breed. The effects
of higher horseshoe crab populations on the size of sea bird populations is
delayed by the time it takes to reach nesting grounds, lay eggs, raise offspring, and return to feed on horseshoe crab eggs . The feedback from
changes in sea bird populations to horseshoe crab populations that was
triggered by an initially higher horseshoe crab population is felt a year
later in the crab population when the now larger number of sea birds prey
on the eggs of the horseshoe crabs .
Systems modelers pay special attention to nonlinearities and time lags in
their models . Throughout their lifetimes, they try to sharpen their perception of nonlinearities and other systems features, and they improve their
skills in modeling them . The eloquence of their models can inspire other
modelers and open their eyes to see the world in a new way.
1.5. Using Dynamic Modeling to Generate Consensus
The intricacies of many real-world systems can overwhelm the ability of humans to adequately understand them . Much of our reasoning is based on
the identification and comparison of patterns, instead of logical inference.
We look at a new experience and try to match it with similar experiences in
1. Introduction
Typically, systems exhibit both positive and negative feedback processes
that have different and varying strengths. Predator-prey relations are a case
in point. The increase in prey population will mean a tendency to produce
even more prey . This is a positive feedback. Similarly, an increase in the
number of predators means that more predators can be born . The negative
feedback is present in the interaction between the two populations, and the
strength of this feedback depends on what happens with each of the two
populations. One possible outcome is a continuous fluctuation in both
populations, which neither settle down to a long-term steady-state, nor result in explosive dynamics.
Variation in the strength of feedback processes are often reflected in
nonlinear relations among system components. Such nonlinear relations
are present if a control variable does not depend on other variables in a linear fashion , but changes, for example, with the square of some other variable. As a result of nonlinear feedback processes, systems may exhibit complex dynamic behavior.
Another source for changes in the strength of a feedback through time
are the delays by which one component changes in response to changes
in another component. In some cases, the length of the time lag is rather
well known. For example, an increase in horseshoe crab populations
means an increased number of eggs being laid in a bay, and thus greater
food supply for sea birds. An increase in food supply translates fairly
quickly into higher body mass of the birds , but also has time-delayed effects on the population dynamics of birds. Well-fed birds are more likely
to survive migration and are more likely to successfully breed. The effects
of higher horseshoe crab populations on the size of sea bird populations is
delayed by the time it takes to reach nesting grounds, lay eggs, raise offspring, and return to feed on horseshoe crab eggs . The feedback from
changes in sea bird populations to horseshoe crab populations that was
triggered by an initially higher horseshoe crab population is felt a year
later in the crab population when the now larger number of sea birds prey
on the eggs of the horseshoe crabs .
Systems modelers pay special attention to nonlinearities and time lags in
their models . Throughout their lifetimes, they try to sharpen their perception of nonlinearities and other systems features, and they improve their
skills in modeling them . The eloquence of their models can inspire other
modelers and open their eyes to see the world in a new way.
1.5. Using Dynamic Modeling to Generate Consensus
The intricacies of many real-world systems can overwhelm the ability of humans to adequately understand them . Much of our reasoning is based on
the identification and comparison of patterns, instead of logical inference.
We look at a new experience and try to match it with similar experiences in