Homework 2 Solutions _ LIFESCIENC 30B mathematics for life science

Homework 2 Solutions Rubric 4 problems were graded in the following scale for a total of 10 points. 4.1.Exercise 7: (2 points) • 2 points: Have 3 graphs (Trajectory + Time Series for both V and X) AND a description of the trend of the graph as the value of a changes • 1 point: Either the description is missing or one of the graphs is missing • 0 point: Blank answer 4.1.Further Exercise 2: (2 points) • 2 points: Able to state that the trajectory will never reach the limit cycle attractor along with a detailed explanation OR state that the trajectory will reach the limit cycle attractor but demonstrate a good effort to explain their answer • 1 point: Missing a detailed explanation • 0 point: Blank answer 4.2.Further Exercise 1: (4 points) Part a: (2 points) • 2 points: Able to identify negative feedback loop • 1 point: Any other kind of answer • 0 point: Blank answer Part b: (2 points) • 2 points: A detailed explanation that will address either sensitivity of the system or time-delay • 1 point: An explanation that somewhat lacks in effort (e.g. state a solution without much explanation) 1 LS 30B Homework 2 Solutions Jan 26, 2018 • 0 point: Blank answer 4.4.Exercise 8: (2 points) • 2 points: Produce a graph with two nullclines + four test points (along with their respective vectors) + some sort of mathematical calculations (even some numbers or algebraic expressions are fine) • 1 point: Produce a graph with two nullclines + four vectors but missing some sort of mathematical calculations (numbers or algebraic expressions) • 0 point: Unable to produce a graph 2 LS 30B Homework 2 Solutions Jan 26, 2018 Chapter 4.1. Exercise 4.1.7. Simulate the model X0 = V V 0 = −X − (aV 3 − V ) for three different positive values of a and compare the trajectories and time series Trajectories with a = 1, 5, and 11 Time Series for V with a = 1, 5, and 11 Time Series for X with a = 1, 5, and 11 3 LS 30B Homework 2 Solutions Jan 26, 2018 As we can see, the higher the value of a, the smaller the limit cycle attractor will be, thus the smaller the amplitude of the oscillations. 4.1. Further Exercise 1 Is a saddle point an attractor? Justify your answer. Saddle point is not an attractor. It is acknowledged that there exists a line on which all trajectories will approach the saddle point. However, the point, in general, violates the definition of an attractor, which states that: for ALL POINTS in the neighborhood aro