The main dependent variable measured in the model is the membrane potential (millivolts) of two different neurons in a series. You will be able to add excitatory and inhibitory neurotransmitters, and compare how these modulate electrical impulses of the two neurons. Additionally, you will be able to compare the effects of three neurotoxins: Tetrodotoxin, botulinum toxin, and sarin nerve gas. While extremely lethal, these toxins are very instructive in understanding neurons because of the specific way the toxins act. Each toxin modifies or inhibits a specific molecule in neurons that help process and transmit information.
Each year, the cost of a college education continues to rise and more and more students must turn to student loans to complete their education. But as graduates leave college to embark on their careers, they face an almost Sisyphean struggle with student debt, forever facing an uphill battle while carrying a heavy burden, only to find they are getting nowhere! Whether you are graduating from college or just entering, we hope this model will enable you to better understand student loans and help plan for your future.
This is our first model in the From Imagination to Simulation series. It is a nod to the Halloween season and investigates a zombie apocalypse! Our fascination with zombies continually grows with the help of movies, TV shows, and books that give a wide range of zombie possibilities. But what are the dynamics behind a zombie epidemic? This model will specifically look at the spread of a zombie outbreak and examine some of the variables that help and hinder the rate of infection. We hope you will continue to see the benefits and versatility of Systems Thinking and enjoy our new series, From Imagination to Simulation! Continue to ponder those out-of-the-ordinary problems. They may seem unrealistic, but perhaps some of their dynamics may resonate with reality. Check out our zombie apocalypse model to see if there is any chance for human survival!
Do you ever feel like work is taking over your life? Burnout is generally characterized as a state of mental and physical exhaustion resulting in low productivity and de-personalization and is most likely caused by prolonged stress that does not dissipate. There are many different aspects that affect both the building and dissipation of burnout. This model focuses on workloads and vacations to see how they contribute to both your level of burnout and productivity. Use this model to ask questions about your workload and any benefits you would receive from taking a vacation. What happens when you suddenly have a bigger workload? What happens when work piles up? Does vacation increase or decrease your stress levels?
Simulation allows students to test the transformation principle. Two major goals of the experiment are: 1. Allow users to see that supernatant from heat-killed bacteria can transform the genes of another bacterium. 2. What transforms the inheritance of the bacteria is DNA, not RNA or proteins.
This model shows the typical plasma concentration profile associated with the administration of several doses of a drug over time. It demonstrates the determinants of the fluctuation in the plasma concentrations, the accumulation of the drug over the course of therapy and the resting steady state plasma concentrations.
Nonlinear or capacity limited pharmacokinetics can occur whenever a process involved in the absorption, distribution or elimination of a drug becomes saturated. This model demonstrates nonlinear elimination (metabolism) using phenytoin as the model drug. Specifically, it demonstrates how increasing doses of the drug produce disproportionate increases in the plasma concentration. It also demonstrates how the model parameters, Km and Vmax influence of the plasma concentration -time profile.
White-eyed is an allele that results in a fly white eyes. Wild-type variants have red eyes. The goal of this simulation is to determine the pattern of inheritance for the white-eyed phenotype. Is yellow body dominant or recessive? Sex-linked or autosomal? Complete, incomplete, or codominant?
Most commonly people take oral doses of a drug over an extended period. This model demonstrates the unique plasma concentration profile associated with this type of drug administration. The model assumes first-order drug absorption with no lag time. Simulations can be carried out to observe how the rate and extent of absorption (bioavailability) affect the profile.
Karner Blue butterfly is an endangered species. Habitat loss and climate change are contributing factors to the reduction in the butterflies' population sizes. Climate change can alter the timing of lifecycles. When climate change disproportionally affects the timing of life cycles of species in an ecosystem asynchrony within a food web occurs.
Apterous is an allele that results in a fly without wings. Wild-type variants have normally functioning wings. The goal of this simulation is to determine the pattern of inheritance for the apterous phenotype. Is apterous dominant or recessive? Sex-linked or autosomal? Complete, incomplete, or codominant?
Use this learning lab to investigate the housing crisis. Play with interest rates as if you are Chairman of the Federal Reserve and see the impact on housing supply and demand. What happens when banks relax mortgage requirements and more people qualify to buy homes?
A look at disaster relief under uncertain local government scenarios. It looks at how long it might take to establish clean water thru flying in bottled water and constructing wells. There is also the impact on spread of disease and survival due to lack of water. Created by Mark Heffernan and George McDonnel
The model shows the unique plasma concentration-time profile associated with the administration of a drug using multiple short infusions. It demonstrates the influence of the duration of the infusion and allows the user to practice the calculation of a suitable dose and dosing interval to achieve desired peak and trough plasma concentrations of a drug.
This is the model that is most commonly used to for the time course of drug effects in man. It assumes that the response is driven by the blood or plasma concentrations of the drug. When the model parameters are known, it can be used to predict response at anytime time after any dose.
Explore a consulting firm’s headcount strategy. Understand the relationship between growth rates, promotion times, headcount pyramid ratios, and attrition rates. This model is based on actual work that was done with a very well-known consulting company (here, code-named TWBC, Inc.). The firm's strategic goals were well-articulated, and each made sense when written down in a list on a piece of paper. However, when subjected to the more rigorous, dynamic scrutiny that an iThink modeling effort provides, the goals (as is too often the case) turned out to be in conflict with one another--stimulating actions that worked at cross-purposes. Efforts to achieve one goal drove the firm farther away from achieving the others. The subsequent analysis conducted with the model also pointed the way toward resolving the internal strategic inconsistencies and putting the firm back onto a strategically sound growth path.
Agriculture offers many modeling opportunities. In this Systems in Focus, we look at the life cycle of a dairy herd, including milk production. This model could be used as the basis for methane production control, trade agreements about milk and how that impacts herd size, increasing production with demand, etc. Visit https://iseesystems.com/resources/systems-in-focus/agriculture/ for more information.
Innovation often raises concerns about job losses, increasingly so in the past century with widespread automation and advanced artificial intelligence. Should we start to fear for our job security or will the creative potential in society maintain the labor force? Explore this model to see some of the interesting possibilities!
Congratulations! You've just been hired by the major grocery chain The Price Shopper as head of marketing. Your job is to turn around The Price Shopper's dismal sales of laundry detergent. The big-wigs have given you 12 months and a marketing budget of up to $10,000 per month to spend as you please. They'll decide to keep you, or send you to the cleaners based on how much profit you bring in over the year. Do you think you can make the big MONEY?
A very simple, one stock, simulation of campus sexist attitudes toward rape and initimate partner violence. The model was originally developed in 1998 and later translated into Stella. The model has a number of modeling errors, but at the time, proved useful for gaining insight into the dynamics of the system and developing an innovative prevention program.
This simulation gives the user the ability to specify their own current condition (weight, age, height etc.), choose their exercise regime and eating plans. The simulator then gives a projection for the user's weight for the next year (at a weekly resolution). Please take note that most of the pictures are navigation buttons to different screens, so remember to click on the pictures. I have personally used this simulator to successfully lose more than 20 kg. Hope you find this as valuable as I did. Good luck with your weight journey!
Business cycles are a fact of life for many industries. Market demand peaks one year only to plummet a year or two later. In this case study of a semiconductor business, Henk Akkermans, Professor of Supply Network Dynamics at Tilburg University, explores different policy options for order handling, production planning and capacity management to reduce oscillation and improve system performance.
Este modelo es un primer intento de utilizar el "Business Canvas" desarrollado por Alexander Osterwalder e Yves Pigneur, para explicar su carácter sistémico mediante la simulación de un modelo de negocio genérico utilizando Stella Architect. El objetivo principal es mostrar el vínculo entre los conceptos del pensamiento sistémico y la práctica del "Systems Dynamics" con el ampliamente difundido "Business Canvas". En la narrativa utilizada para describir la construcción del diagrama "Stock & Flow", se denomina entre parentesis el tipo de componente (Stock, Flow, Converter, o Conector) correspondiente a los principales elementos del modelo de negocio. La simulación permite visualizar la naturaleza sistémica de un modelo de negocio representado mediante el "Business Canvas".
Some drugs do not directly produce the measured drug response. Instead they act upstream, and either increase or decrease the amount of the entity that directly mediates the response (response variable). Indirect effect Model I can be used for drugs that inhibit the synthesis of the response variable. An example is warfarin which inhibits the synthesis of clotting factors.
This model is an extension of the Simple Agrarian Society model from Dynamic Systems. The extensions are to add a CO2 cost to the industrialization, an impact of CO2 on global temperature, an impact of global temperature on drought frequency, and impact of drought on food production and an impact of global temperature on polar sea ice.
Some drugs act by binding covalently to their receptors. As a result, the target is destroyed and its function returns only when it has been replaced by newly synthesized product. The target may be a protein, DNA, an enzyme, or a cell at any stage of development. This model has been applied to the action of the proton pump inhibitors, which bind to and destroy the H+,K+-ATPase pumps in the parietal cells of the gastric mucosa. Normal proton secretion is restored only when the pumps are replaced by newly synthesized functioning pumps (i.e., the usual turnover time of the system).
This simple model explores the demand dynamics for a state's energy usage. For three sectors (residential, industrial, and agricultural) you can adjust the size of initial user base, the growth rate for the number of users, and the rate for the change in demand per user.
An Introduction to SysQ is our free interactive resource for building and applying Systemic Intelligence (SysQ). By using this guide, practitioners of systems thinking and adaptive leadership will better understand why systemic intelligence is an essential leadership capacity and how to increase anyone's (or any team’s) ability to apply it. An Introduction to SysQ gives you rapid access to the full suite of systems thinking tools (including the SysQ Questions, trend graphs, archetypes, causal loop and stock & flow diagrams, and simulations) – including when and how to use each! And because the guide is browser based, it works on mobile devices! You can even embed it on your website. We believe you’ll find this resource so useful that you’ll decide it belongs in your browser’s favorite bookmarks! (Currently, it works best on Google applications and devices – Chrome and Android-based devices.)
A country builds its empire by attacking its neighbours and taking over both their land and their people. The larger the empire becomes, the more resources they have available to take further territory by force. However the further they expand, the harder they find it to keep expanding due to the geographical and organisational logistics involved. Additionally the empire finds it harder to maintain social cooperation among its people, its asabiya.
En este simulador, Usted juega el papel del director de una planta de producción de la emtresa magallanes. Debe manejar el personal de venta y la capacidad de producción de modo a obtener un crecimiento fuerte y sostenido de las ventas.
Change image Submit your own comment on the simulation. Share Comment upgrade hosting plan delete simulation Transit Compartment Model of Drug Response By Sara Rosenbaum Sim URL: https://forio.com/simulate/sarar/transit-compartment-model Sim access:Other authors can download source model Sim plan: Simulate Free Sim stats:This sim has been run 326 times. This simulation was uploaded to Forio Simulate with the isee NetSim software. More information can be found at iseesystems.com. Your Rating: 1 star2 star3 star4 star5 star Average Rating: rating(1) Click here to edit the description A delay in response to a drug can occur when it takes a long time for the drug’s initial effect to be translated into the final response (a long transduction process). The delayed response profile can be captured using a series of transit compartments.
Experience the dynamics of making a business shift from traditional to e-commerce. Simulate different scenarios for how you’ll allocate spending on marketing versus infrastructure. You will see one of the more common dynamics in making a business shift, what Systems Thinkers refer to as the "worse before better" dynamic. If initial investments are made in the infrastructure quality rather than in marketing, total customers will actually fall for awhile. But if increasing amounts are spent on marketing (once the infrastructure is in place) then total customers will begin to explode. And the transition becomes successful!
Model Mysteries Chapter 1: Growing, Growing, Gone Model 3: Zombie Chickens Dare
Model Mysteries Chapter 7: Fix it Fun Hatfields - Fixed
One organization in the service delivery business experienced a situation where the number of delivery requests increased dramatically due to a seasonal promotion. This increase in requests caused an overload on the service delivery staff by not only having more people requesting service, but also because the amount of time spent with each customer increased. This model is designed to describe why this occurred in a way that can be transferable to other service delivery organizations.
Model Mysteries Chapter 3: Mind the Gap Dare 3
Model Mysteries Chapter 7: Fix it Fun Base Model
The model is suppose to help, learn and investigate the flow of carbon between the atmosphere and land plants and soils through photosynthesis and respiration. The key questions we want to understand are: ● How does the plant fertilization feedback work? ● Are plants taking up a significant amount of the carbon humans are emitting? ● Can we solve the climate change problem by planting trees to take up our CO2?
Model Mysteries Chapter 1: Growing, Growing, Gone Model 2: Zombie Chickens
Keystone species are defined as a plant or animal that plays a unique role in the way the ecosystem functions. But what would happen if that species were removed? What ripple effects would be caused by the absence of this species? We can examine these questions by looking at the wolf population in Yellowstone National Park. Wolves once flourished in Yellowstone and its surrounding areas. However, soon after the area was settled, misperceptions caused by fear and hatred fueled a large extermination effort of the wolves. For nearly 70 years, wolves were absent from Yellowstone. During this time, the ecosystem changed and diminished until scientists realized the value of the wolves and reintroduced them to Yellowstone. This model, built in iThink, uses storytelling to understand the dynamics of this keystone species. What animals were affected by their presence or absence. See how wolves play a part in not only population control of their prey but other animals and even plants far down the trophic levels.
Tolerance may be defined as a process that results in a reduction in the response to a specific drug concentration following repeated drug exposure. Tolerance could occur if an endogenous compound that plays an essential role in the response chain becomes depleted during response. This model assumes the drug stimulates the production of a response variable which becomes then becomes depleted.
Model Mysteries Chapter 6: Stuck in a Rut Story 2
Model Mysteries Chapter 2: Mind the Gap Base Model
Model Mysteries Chapter 5: The Disappeared Part 2
Suppose we have a bucket sitting under a tap with water flowing into it at a constant rate. The bucket has a hole in the bottom, so water leaks out over time. The rate at which water flows out of the hole won't be constant because the water pressure at the bottom depends on the height of the water in the bucket. Therefore, if the bucket is nearly empty, only a trickle will escape, but if the bucket is full, the extra weight of the water will push the water out of the hole much faster. Also, if the hole is bigger, the water will flow out much faster. For this model, we're going to assume that the outflow rate is proportional to the volume of water in the bucket multiplied by the size of the whole: Out_flow = Volume_In_bucket * Size_of_hole
This model shows the typical effect of several anticancer drugs on the number of circulating neutrophils. The drugs destroy neutrophils as they develop in the bone marrow, and its takes several days for their action to affect the circulating neutrophils. The model demonstrates how inter-individual variability in pharmacokinetics and pharmacodynamics can effect the magnitude and duration of this response.
Suppose we have a bucket sitting under a tap, with water flowing into it at a constant rate. The bucket has a hole in the bottom, so water leaks out over time. The rate at which water flows out of the hole will not be constant because the water pressure at the bottom depends on the height of the water in the bucket. Therefore if the bucket is full, the extra weight of the water will push the water out of the hole faster. Also if the hole is bigger the water will flow faster. For this model, we're going to assume that the outflow rate is proportional to the volume of the water in the bucket multiplied by the size of the hole.
Some drugs do not directly produce the measured drug response. Instead they act upstream, and either increase or decrease the amount of the entity that directly mediates the response (response variable). Indirect effect Model 2 can be used for drugs that inhibit the degradation of the response variable. As a result they increase the amount of the response variable.
Yo listen up, here's the story About a little guy that lives in a blue world And all day and all night and everything he sees is just blue Like him, inside and outside Blue his house with a blue little window And a blue Corvette And everything is blue for him And himself and everybody around 'Cause he ain't got nobody to listen I'm blue da ba dee da ba daa Da ba dee da ba daa, da ba dee da ba daa, da ba dee da ba daa Da ba dee da ba daa, da ba dee da ba daa, da ba dee da ba daa I'm blue da ba dee da ba daa Da ba dee da ba daa, da ba dee da ba daa, da ba dee da ba daa Da ba dee da ba daa, da ba dee da ba daa, da ba dee da ba daa I have a blue house with a blue window Blue is the color of all that I wear Blue are the streets and all the trees are too I have a girlfriend and she is so blue Blue are the people here that walk around Blue like my Corvette, it's in and outside Blue are the words I say and what I think Blue are the feelings that live inside me I'm blue da ba dee da ba daa Da ba dee da ba daa, da ba dee da ba daa, da ba dee da ba daa Da ba dee da ba daa, da ba dee da ba daa, da ba dee da ba daa I'm blue da ba dee da ba daa Da ba dee da ba daa, da ba dee da ba daa, da ba dee da ba daa Da ba dee da ba daa, da ba dee da ba daa, da ba dee da ba daa I have a blue house with a blue window Blue is the color of all that I wear Blue are the streets and all the trees are too I have a girlfriend and she is so blue Blue are the people here that walk around Blue like my Corvette, it's in and outside Blue are the words I say and what I think Blue are the feelings that live inside me I'm blue da ba dee da ba daa Da ba dee da ba daa, da ba dee da ba daa, da ba dee da ba daa Da ba dee da ba daa, da ba dee da ba daa, da ba dee da ba daa I'm blue da ba dee da ba daa Da ba dee da ba daa, da ba dee da ba daa, da ba dee da ba daa Da ba dee da ba daa, da ba dee da ba daa, da ba dee da ba daa
Some drugs do not directly produce the measured drug response. Instead they act upstream, and either increase or decrease the amount of the entity that directly mediates the response (response variable). Indirect effect Model IV can be used for drugs that stimulate the degradation of the response variable. As a result they decrease the amount of the response variable.
it is a model for the adoption of a new technology, Given P as the potential adopters of the new technology, and A as the actual adopters, the adoption of new technology takes place due to two process - 1) word of mouth and 2) advertising and any other external influence. the adoption rate AR from potential adopters is AR= WoM + AfA
Model Mysteries Chapter 2: Energy Drink Mania Model 1: Basic Model
Can Energy Prices Really Be Passed on to the Consumer? Energy literally fuels every aspect of today's economy. When energy costs increase, many businesses will increase prices thereby "passing on" the cost to consumers. This story helps to explain some of the broader reaching impacts of such a policy. This model was created by Steve Peterson.
This model depicts a process with exogenous inflows where the efficacy of the process descreases in proportion to time spent in the process. It is followed by a quality control mechanism with sensitivities and specificities which also decrease with time spent in the quality process. This bounded process and quality control is then checked against a gold standard which then adjusts as necessary in alignment with larger policy goals and feeds a larger data set. This model represents a realistic vision of what frontline quality control mechanisms should exist in the healthcare delivery system. It can be used as a tool for policy making to determine what acceptable rates of efficacy and outcome can be tolerated as quality based payments grow in popularity.
A self reliant food system model at the community scale
This model is a second extension of the Simple Agrarian model from Dynamic Systems that modifies the simple agrarian society model to include drought, industry produced CO2 and ice sheet dynamics. Primarily this is published as a test of porting from Stella 10.1 and learning how the new Stella Online operates. Several of the converter weights have been fine tuned to provide a better behaved model than the first adaptation. At some point a user interface and story will be added and the starting conditions calibrated to approximate treating Earth as an industrialized, agrarian society.
Explore the laws of thermodynamics with this animal temperature model. As you experiment, think about animal adaptations and consider the following: What problems do small animals face compared to large animals in hot and cold environments? What problems do cold-blooded (poiklothermic) animals face compared to warm-blooded (homeothermic) animals? What is it that insulation really does for animals? The story behind this model is explained in a chapter of Tracing Connections
This is the second version of the simulation that analyzes the interactions among the six Sustainable Development Goals (SDGs) that are the focus of the Second Annual Multi-stakeholder Forum on Science, Technology, and Innovation for the Sustainable Development Goals (STI Forum). The interface can be used to understand the trade-off due to the complex interplay among the set of six SDGs
Market-capitalism typically goes through cycles of expansion and contraction. Every now and then, these common economic cycles go off the hinges. They become unstable and can lead to recessions, crises and depressions—phenomena that economists typically look to exogenous forces to explain. Alternative, mostly Marxian and Keynesian, explanations for the instabilities have been sought within the structure of the economic system itself. One such explanation is provided by Steve Keen in his Goodwin-Minsky model. The model effectively mimics the dynamics of key indicators prior to, during and after the 2007/08 crisis. However, the model is also over-specified, highly sensitive to initial conditions and therefore more difficult to convey. In line with George Box’s plea for parsimony, this paper presents a more straightforward version of Keen’s model that remains consistent with its fundamental behaviour. The model also illustrates the potential for further dialogue between Marxian economics and system dynamics.
The model was developed in a company of the Agri-food sector and considers the distribution link in the collection center of the Tomato Roma product for export to Rio Rico AZ, in 2017 by students of the Technological Institute of Sonora of the Department of Industrial Engineering.
In a pioneering attempt, isee systems hosted a Community Model Building webinar on Drought in California, a severe and complex issue facing humanity. We discussed live with the community what the main problem variables are and how they change over time. We then built a qualitative model (causal loop diagram) based on participants' input. This quantitative model (stock and flow diagram) model was built in the background, representing the discussion.
Some drugs do not directly produce the measured drug response. Instead they act upstream, and either increase or decrease the amount of the entity that directly mediates the response (response variable). Indirect effect Model III can be used for drugs that stimulate the production of the response variable. As a result they increase the amount of the response variable.
Model Mysteries Chapter 5: The Disappeared Dare 3
Model Mysteries Chapter 4: Spreading Like Crazy Base model
Model Mysteries Chapter 2: Energy Drink Mania Story 2: Medicine
In the Fish Banks, Ltd. game (originally developed as a board game by Professor Dennis L. Meadows in 1986), teams of players manage their own fishing companies. At the beginning of the game, each fishing company has equal financial resources and fishing fleet. Each company has the same operating costs and technology. At the beginning of every simulated year, the companies make decisions about building, buying, and/or selling ships, whether to fish or not, and how far to send their fleet for fishing. The game's objective is to maximize total assets at the end of the simulation. The game developed here is a modified version of the Meadows' game as explained in the game rules.
Model Mysteries Chapter 4: Spreading Like Crazy Dare 3
The dynamic model shall explain the rapid diffusion of the lionfish - an invasive species - throughout the Caribbean Sea and the Atlantic Ocean. The interface contains two explanatory models - a simple diffusion model and more realistic convection model - as well as a policy game to manage the regional countermeasures of local decision makers.
One of the most challenging tasks in most organizations is the allocation of headcount between time-competing activities. In this model, you will have a chance to explore these sorts of dynamics in the context of a consulting firm, where the same headcount can be allocated to business development activities and client service delivery. You'll see the classic pattern of "Feast or Famine," or the so-called "pig in a snake," emerge.
Model of the interaction between Slbo and Trbl. C/EBP encoded by Slbo binds Trbl and is subsequently tagged by uiquitination. This interaction also changes the function of the pseudokinase domain of Trbl. In result, Trbl becomes susceptible to small molecule binding and is degraded.
Model Mysteries Chapter 2: Energy Drink Mania Story 2: Sheep
This simulation shows the basic dynamics of a hospital emergency room. Patients arrive, are treated and leave. You are able to control the average arrivial rate and average treatment time. This simulation was made using the 3rd party developer API embedded within Stella Architect.
Level A: Up and Down in the Wild: Predator and Prey This lesson allows students to explore the interactions of two animal populations (wolves and moose) within an ecosystem. One animal in the simulation is a predator. The other animal is its prey. Their populations rise and fall (oscillate) over time as they interact and impact one another.
The Bass Model or Bass Diffusion Model was developed by Frank Bass and it consists of a simple differential equation that describes the process of how new products get adopted in a population. The model presents a rationale of how current adopters and potential adopters of a new product interact.
What is most effective in controlling the outbreak of a flu virus in schools? Is it better to vaccinate or stay home? Use this Learning Lab to understand how infectious disease spreads and why the World Health Organization signaled the 2009 H1N1 (also called “swine flu”) outbreak as a pandemic.
The flows of light energy toward and away from the Earth. Energy comes in from sunlight, but some of its reflected back away from Earth, depending on the planet's albedo. The rest is absorbed by the Earth's surface and stored there. The Earth's surface gives infrared blackbody radiation according to the Stefan-Boltzmann law. A balance is reached when the inflowing solar energy exactly equals the outflowing infrared energy.
On July 24th, 2009 the Car Allowance Rebate System (CARS), commonly known as "Cash for Clunkers," began processing rebate claims. The $1 billion appropriated for the system was exhausted just SIX days later. This simulation explores an alternative program that is self-sustaining AND reduces automobile emissions. Using a combination of fees and rebates this program can finance itself (no emergency appropriations from Congress), reduce gasoline consumption (putting cash back in consumer's pockets), AND contribute to cleaner air for us all!
Model Mysteries Chapter 2: Energy Drink Mania Story 1: Trees
Model Mysteries Chapter 7: Fix it Fun Base model
An agrarian population can exceed its normal carrying capacity by the formation of a state that helps improve land productivity. As the population and state grow, it becomes harder for state revenue to stay ahead of expenditure. Eventually the state runs out of money and collapses, with a large drop in population numbers.