I’m working on a differential equations discussion question and need an explanation to help me study.

1. Watch the lecture by Dr. Gloria Ladson-Billings. It is about one hour and twenty minutes. Write a half-page single space reflection.

2. In the climate change problem there was an inherent feedback loop that, when the de-regulation parameter changed, the system was bumped into a new normal (which is not a better new normal for the planet). As you saw, this new normal is not easily reversed. This phenomenon is known as hysteresis, which represents the history dependence of physical systems. If you push on something (or change a parameter in the system), it will yield: when you release (or reset the parameter), does it spring back completely? If it doesn’t, it is exhibiting hysteresis.

Pick one of three contexts below and discuss how the context might reflect a similar situation where a parameter change could bump the system into a new normal, one that is not easily reversed. Create a hypothetical phase line and explain how the phase line describes the context.

Context 1: The parameter k is related to the ratio of counselors to cops and the dependent variable is high school graduation for historically marginalized students.

Context 2: The parameter k is related to shifting funding from law enforcement to social programs (housing security, food security) and the dependent variable incarceration rate of historically marginalized groups.

Context 3: (Un)employment in times of economic downturn. See Wikipedia entry: 7.1 Permanently higher unemployment