Cubic population model
Not what you're looking for?
Consider the cubic population model
dN/dt=cN(N-?)(1-N)
Where c and ? are given constants, such that c>0 and 0<?<1. Note that the population N is measured in units of thousands.
Find and classify the steady states N_1<N_2<N_3 of this equation.
If the initial population is N_0 describe, without proof, the future of the population, distinguishing various cases on the size of N_0 relative to the steady states N_1,N_2 and N_3.
Obtain the solution of the differential equation with initial condition N(0) =2, assuming the parameters c=1 and ?=1/2.
Hints: If you encounter a quartic equation for N, consider the substitution K=N-1/2. For choosing the right signs in extracting roots, you should assume Nâ?¥1.
Purchase this Solution
Solution Summary
Cubic population model is clearly exemplified in this solution.
Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Probability Quiz
Some questions on probability