Introduction to Systems Analysis!

Lecture 02

August 23, 2023

Review of Last Class

Last Class

Went through course syllabus and policies.

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Why Study Systems?

What Is A System?

A system is:

“an interconnected set of elements that is coherently organized in a way that achieves something…

A system must consist of three kinds of things: elements, interconnections and a function or purpose.”

— Donella Meadows, Thinking in Systems: A Primer, 2008

Examples of Systems

Can we think of any examples of systems?

What about things that are not systems?

Why Are Systems Interesting?

In other words, a system involves an interconnected set of components.

Those interconnections can lead to very different dynamics and outcomes than if the component processes were studied in isolation.

This is called emergence.

Key Definitions

System State

System State: quantities or variables which evolve over time based on external inputs and system dynamics.

The state gives you a “snapshot” of the system at a given point in time.

Stocks and Flows

  • A stock is the amount of a system property: concentrations of a pollutant, numbers of currency units, etc.
  • A flow is the way in which a stock changes: decay, diffusion, production, consumption, etc.

Modeling Flows

For example:

  • Mass balance equations let us track changes in stocks at particular points;
  • Equilibrium conditions are requirements that there is no net flow, and thus that stocks are preserved;
  • Fate and transport modeling involves quantifying how stocks change as they move through the system.

Feedback Loops

One example of an emergent systems dynamic is a reinforcing (positive) feedback loop, where a shock to the system state gets worse.

Feedback loops can also be dampening (negative), where a shock is weakened.

Ice-Albedo Feedback Loop

Tipping Points

Another important systems concept is a tipping point, where the system changes states abruptly and drastically.

Examples include lake eutrophication and ice-sheet melting.

Figure 1: Lake eutrophication dynamics based on the shallow lake modelwithout additional inputs. The black line is the P recycling level (for $q=2.5), which adds P back into the lake, and the dashed lines correspond to differerent rates of P outflow (based on the linear parameter \(b\)). The lake P level is in equilibrium when the recycling rate equals the outflows. When the outflow is greater than the recycling flux, the lake’s P level decreases, and when the recycling flux is greater than the outflow, the P level naturally increases. The red lines show the direction of this net flux.

Systems Analysis

Systems Analysis Overview

What We Study

  • System dynamics;
  • Response to inputs;
  • Alternatives for management or design.

Needs

  • Definition of the system
  • Systems model

What Do We Need To Define A System?

  • Components: relevant processes, agents, etc
  • Interconnections: relationships between system components
  • Control volume: internal vs. external components
  • Inputs: control policies and/or external forcings
  • Outputs: measured quantities of interest

Key Takeaways

Key Takeaways

  • A system is an interconnected set of components.
  • Systems are interesting because interconnections can result in unexpected outcomes.
  • Key terms:
    • state
    • stocks
    • flows

Key Takeaways

  • To define a system, need to specify:
    • components
    • interconnections
    • control volume
    • external inputs
    • outputs of interest

Upcoming Schedule

Next Classes

Friday: Work on Lab 1.

  • Preparation:
    • Follow the steps in Tools Setup to get GitHub and Julia set up.
    • Click the Lab 1 link in Ed Discussion to link your GitHub account to the class roster and create your Lab 1 repository.

Next Classes

Monday: Modeling Systems