# James C. Clements: Week 3

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## Terminology

• Dynamical System: "A system that changes over time according to a set of fixed rules that determine how one state of the system moves to another state." [1]
• Law of Mass Action: "The law that states the following principle: the rate of a chemical reaction is directly proportional to the molecular concentrations of the reacting substances" [2]
• Homeostasis: "The ability of a system or living organism to adjust its internal environment to maintain a stable equilibrium; such as the ability of warm-blooded animals to maintain a constant temperature." [3]
• Equilibrium: "The condition of a system in which competing influences are balanced, resulting in no net change." [4]
• Oscillation: "A regular periodic variation in value about a mean" [5]
• Autocatalysis: "Catalysis in which the catalyst is one of the products of the reaction" [6]

## Applying the Law of Mass Action

• Construct differential equations that model the following reactions. Be sure to define your state variables and rate constants.
1. A + BC
2. A + BC
3. A + B ↔ 2C
4. 2A + 3BC+D

Please note that the symbolis used to denote arrows (reactions) in both directions.

## Simulating Reaction Kinetics

1. E + SESE + P

that we have studied in class. Set the parameters as follows:

• [S0] = 1.0
• [E0] = 0.2
• [ES0] = 0.0
• [P0] = 0.0
• k1 = 2.0
• k-1 = 0.0
• k2 = 10

Plot the output, and save the plot as an image. Post the image on the wiki as the answer to the question.

Simulation of Reaction Kinetics