Browse quantitative models header
There follows a list of quantitative models in the SES Library.
| Title | Type |
|---|---|
Lorenz Model | Model |
| This simple model was developed by Edward Lorenz in 1963 to study fluid mechanics (based on Navier-Stokes equations). It is the first ever model of a chaotic dynamical system. Chaos arises when a deterministic, nonlinear dynamical system exhibits long-term unpredictability in behavior due to sensitivity to initial conditions.The model is a three-dimentional system of differential equations. Specifically, the model describes the convection motion of a fluid in a small idealized "Rayleigh-... | 09 Aug 2016 |
Waterwheel Model | Model |
| This model describes the dynamics of a waterwheel. The wheel has 10 cups that are filled when as they pass over the top of the arc of the wheel (imagine a Ferris wheel where instead of seats there are buckets. Water is flowing down on the Ferris wheel filling the buckets). The weight of the water makes the wheel turn. However, in this model, the buckets leak. So if the flow of the water from the top is too slow, some interesting motion can occur. This waterwheel model is a perfect physical... | 09 Aug 2016 |
Brander-Taylor Model | Model |
| This is the original Brander-Taylor Easter Island model. Brander and Taylor (1998) describes the model as the following: "The paper presents a general equilibrium model of renewable resource and population dynamics related to the Lotka-Volterra predator-prey model, with man as the predator and the resource base as the prey. We apply the model to the rise and fall of Easter Island, showing that plausible parameter values generate a 'feast and famine" pattern of cyclical adjustment in... | 09 Aug 2016 |
Pezzey-Anderies Model | Model |
| This model describes the Pezzey-Anderies extension to the Brander-Taylor Easter Island model. In addition to the parameters in the Brandor-Taylor model, Pezzey and Anderies have introduced $tax$ and $h_m$. Pezzey and Anderies (2003) gives the following overview: "We extend the Brander–Taylor model of population and resource development in an isolated society by adding a resource subsistence requirement to people's preferences. This improves plausibility; amplifies population overshoot and... | 09 Aug 2016 |
Fishery Model | Model |
| This is a standard Gordon-Schaefer model that simulates a simple open-access fishery in discrete time. A fishery stock grows logistically and is harvested by humans. Fishers always exert too much effort and harvest fish at a level that is socially NOT optimal. This happens because fishers are driven to harvest until their net profit drops down to zero. A socially optimal level of harvesting effort is attained when marginal cost of harvesting effort and marginal revenue from harvesting become... | 09 Aug 2016 |
Predator-Prey Model | Model |
| This is a simple predator-prey model with type I or II functional response (depending on parameter choices). The model is also known as the Lotka–Volterra equation. Prey grows logistically and is harvested by predators. In the model, predators are specialists (i.e., they eat only one particular prey species for survival and growth), and their predation pattern can be either type I or II functional response. In type I, the predation rate depends only on the prey density ($b=0$), i.e., how... | 09 Aug 2016 |
Lotka-Volterra Competition | Model |
| Symmetric competition model | 09 Aug 2016 |
Pumpa Irrigation System | Model |
| In this case, the surface water level is modeled by a first order differential equation. There are six sections with equal area that are allocated water based on institutions that determine how long each sector receives water, and in what order. Water is allocated to a given sector by opening and closing gates along the irrigation canals. Based on these allocations, each sector maintains a crop yield depending on the amount of time that maintains their water level within the bounds of a desired... | 09 Aug 2016 |
Robustness, institutions, and large-scale change in social-ecological systems: the Hohokam of the Phoenix Basin | Model |
| This is a model that illustrates the relationship among levels of (1) population, (2) human-made capital, (3) natural capital , and (4) resource consumption. The key insight to be gained from the model is that as the ratio of capitalization in human-made infrastructure over human population is varied in the parameter space, the dynamics of natural capital changes and becomes vulnerable to different disturbance regimes. That is, as humans grow in population and over-invest in capitalization/... | 09 Aug 2016 |
Culture and Human Agro-ecosystem Dynamics: the Tsembaga of New Guinea | Model |
| The model of Tsembaga agro-ecology explores the coupled dynamics involving population growth, renewable resource base, resource consumption by humans, and the self-regulating effect of cultural ritual. The model demonstrates that the cultural ritual of Tsembaga (Kaiko) can stabilize the Tsembaga population and its resource level. This is achieved by attenuating wildly fluctuating limit cycles of population and resource levels down to desirable small-amplitude cycles. Anderies (1998) describes... | 09 Aug 2016 |
Australian Rangelands Model | Model |
| This model tells a story of resilience of a rangeland system in Australia. Anderies et al. (2002) provides the following overview of the model. "We developed a stylized mathematical model to explore the effects of physical, ecological, and economic factors on the resilience of a managed fire-driven rangeland system. Depending on grazing pressure, the model exhibits one of three distinct configurations: a fire-dominated, grazing-dominated, or shrub-dominated rangeland system. Transaction costs... | 09 Aug 2016 |
A Two-Sector Growth Model: Economic Development, Demographics, and Renewable Resources | Model |
| This is a two-sector growth model that couples the dynamics of human demographics and a renewable resource base. The two sectors are agricultural and manufacturing sectors. To capture both the positive (Malthusian) and negative (modern growth) type relationships between population growth and output, it is important to model the shifting composition of output from agricultural to manufacturing as growth occurs. Thus, the model is a two sector (productions and consumptions in... | 09 Aug 2016 |
Analyzing the Impact of Agave Cultivation on Famine Risk in Arid Pre-Hispanic Northern Mexico | Model |
| Here, a simple model of a subsistence economy based solely on the cultivation of maize and agave is presented. While maize is an annual plant that humans can eat and store, agave is a perennial plant that can be used for multiple purposes: as edible materials yielding caloric values and as fiber materials for producing items like clothing, ropes, and baskets. This model tries to capture the essence of a cultivation strategy of a portfolio of plants that have differing levels of sensitivity... | 09 Aug 2016 |
Animated demonstration of the Lorenz Model | Model |
| Animated demonstration of the Lorenz model and its sensitivity to initial conditions. The simulation starts with twenty points very close to each other, and follows them as they move further away. The starting values differ in the fifth and sixth significant digits of a single coordinate. The Lorenz model was developed by Edward Lorenz in 1963 to study fluid mechanics.The model is a three-dimentional system of differential equations. Specifically, the model describes the convection motion of a... | 09 Aug 2016 |
The effect of scaling and connection on the sustainability of a socio-economic resource system | Model |
| Most modeling exercises on resource-population dynamics of a socio-economic system assume that many growth-related phenomena are linearly related to population size. The model presented here departs from this linear thinking by exploring potential non-linear relationships, or power-law scaling behaviors, with population size. For example, twice as many people do not mean that twice as much resources are required to maintain existing population. Similarly, twice as many people do not necessarily... | 09 Aug 2016 |
