To analyse the dynamics of forest in Budworm vs. forest system by interpreting the terms biologically, then to non-dimensionalize the system, sketching the nullclines and then to draw the phase portrait for both large and small values of parameter B. Concept Introduction: Fixed point of a differential equation is a point where, f(x) = 0 ; while substitution f(x) = x ˙ is used and x&*#x00A0;is a fixed point Nullclines are the curves where either x ˙ = 0 or y ˙ = 0 they show whether the flow is completely vertical or horizontal. Phase portraits represent the trajectories of the system with respect to the parameters and give qualitative idea about evolution of the system, its fixed points, whether they will attract or repel the flow etc.

Question

Want to see the full answer?

Answer 1

Question

Chapter 8.1, Problem 10E

Interpretation Introduction

Interpretation:

To analyse the dynamics of forest in Budworm vs. forest system by interpreting the terms biologically, then to non-dimensionalize the system, sketching the nullclines and then to draw the phase portrait for both large and small values of parameter B.

Concept Introduction:

Fixed point of a differential equation is a point where, f(x) = 0 ; while substitution f(x) = x˙ is used and x&*#x00A0;is a fixed point

Nullclines are the curves where either x˙=0 or y˙ = 0 they show whether the flow is completely vertical or horizontal.

Phase portraits represent the trajectories of the system with respect to the parameters and give qualitative idea about evolution of the system, its fixed points, whether they will attract or repel the flow etc.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

The output of a solar panel (photovoltaic) system depends on its size. A manufacturer states that the average daily production of its 1.5 kW system is 6.6 kilowatt hours (kWh) for Perth conditions. A consumer group monitored this 1.5 kW system in 20 different Perth homes and measured the average daily production by the systems in these homes over a one month period during October. The data is provided here. kWh 6.2, 5.8, 5.9, 6.1, 6.4, 6.3, 6.9, 5.5, 7.4, 6.7, 6.3, 6.2, 7.1, 6.8, 5.9, 5.4, 7.2, 6.7, 5.8, 6.9 1. Analyse the consumer group’s data to test if the manufacturer’s claim of an average of 6.6 kWh per day is reasonable. State appropriate hypotheses, assumptions and decision rule at α = 0.10. What conclusions would you report to the consumer group? (Hint: You will need to find Descriptive Statistics first.) 2. If 48 homes in the central Australian city of Alice Springs had this system installed and similar data was collected, in order to assess whether average daily production in…

Fungal Growth Because of the time that many people spend indoors, there is a concern about the health risk of being ex- posed to harmful fungi that thrive in buildings. The risk appears to increase in damp environments. Researchers have discov- ered that by controlling both the temperature and the relative humidity in a building, the growth of the fungus A. versicolor can be limited. The relationship between temperature and rela- tive humidity, which limits growth, can be described by R(T) = -0.00007T³ + 0.0401T² – 1.65727 + 97.086, 15 < T < 46, where R(T) is the relative humidity (in percent) and T is the temperature (in degrees Celsius). Find the temperature at which the relative humidity is minimized. Source: Applied and Envi- ronmental Microbiology.

Consider the following estimated model, where the dependent variable is the log of the hourly wage: log(wage) = 0.417 - 0.238female + 0.17educ + 0.0232 exper - 0.00058exper? +0.0295tenure – 0.00059tenure? female 1 if the person is female, and 0 if the person is male educ = level of education, in years exper = level of expertise, in years tenure = duration of tenure, in years Given that the above regression model has 313 observations, then its degrees of freedom is equal to For the same levels of education, expertise, and tenure, women earn exactly % less compared to men, holding other factors fixed.