Carmen E. Castaneda: Week 3

Look up the following terms and provide definitions. For each definition, three elements are required: you must quote a source, reference the source, and interpret the definition in your own words.

dynamical system: A means of describing how one state develops into another state over the course of time.(1)
law of mass action: A law stating that the intensity of a reaction is dependent on the degree of presence of the reactants responsible for the reaction.(3)
homeostasis: The ability of the body or a cell to seek and maintain a condition of equilibrium or stability within its internal environment when dealing with external changes (2)
equilibrium:The state of balance or static; the absence of net tendency to change.(4)
oscillation: Fluctuation; variation; change back and forth.(5)
autocatalysis: a reaction in which one or more of the products formed acts to catalyze the reaction.(6)

Construct differential equations that model the following reactions. Be sure to define your state variables and rate constants.

A + B → C
- d[A]/dt = -k₁[A]
- d[B]/dt = -k₁[B]
- d[C]/dt = k₁[A][B]
A + B ↔ C
- d[A]/dt = -k₂[A]+k_-1[C]
- d[B]/dt = -k₂[B]+k_-1[C]
- d[C]/dt = k₂[A][B]-k_-1[C]
A + B ↔ 2C
- d[A]/dt = -k₃[A]+k_-2[C]²
- d[B]/dt = -k₃[B]+k_-2[C]²
- d[C]/dt = k₃[A][B]-k_-2[C]²
2A + 3B ↔ C+D
- d[A]/dt = -k₄[A]²+k_-3[C][D]
- d[B]/dt = -k₄[B]³+k_-3[C][D]
- d[C]/dt = k₄[A]²[B]³-k_-3[C]
- d[D]/dt = k₄[A]²[B]³-k_-3[D]

Please note that the symbol ↔ is used to denote arrows (reactions) in both directions.

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