LIFESCI 30A Lecture Notes - Lecture 6: Differential Equation, Tangent Space, Slope Field

• School: UCLA
• Department: Life Sciences
• Course: LIFESCI 30A
• Professor: Conley William Joseph

Document Summary

Seasonal fluctuations are on a large time scale, from one year to the next. Cycles can even be over the course of 10 to 20 years. Movement in state space traces out a curve (trajectory) to visualize behavior of the models. Differential equations: (the model) (use brackets because it"s a system of equations. The function takes [r f] as its input and gives the corresponding change vector as its output. When r = 30 f = 10, you get an r" and an f" from the differential equations r"=3 f"=2. The two arrows form a change vector (right 3, up 2) A change vector for this model has the form [r" (above) f"] *their rate of change. The horizontal component is -3, so left by 3. The vertical component is 5, so up by 5. The point of this is that differential equations provide a number to denote.