Fisher's Equation (I solved it, now need to know how to analyze my plot)

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SUMMARY

The discussion centers on solving Fisher's equation, a partial differential equation represented as ut = uxx + u(1-u). The user successfully solved the equation and generated plots but seeks guidance on analyzing these plots to determine how the wave front speed of solutions is influenced by the initial population amplitude and the spatial interval length occupied by the mutant gene. The conversation highlights the need for methods to extract meaningful relationships from the visual data presented.

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  • Understanding of partial differential equations (PDEs)
  • Familiarity with Fisher's equation and its biological implications
  • Proficiency in data visualization techniques
  • Knowledge of wave front dynamics in mathematical biology
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  • Research methods for analyzing wave front speed in PDE solutions
  • Explore numerical simulation tools for PDEs, such as MATLAB or Python's SciPy
  • Learn about stability analysis in Fisher's equation
  • Investigate the impact of initial conditions on wave propagation in biological models
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Mathematicians, biologists, and researchers interested in mathematical modeling of population dynamics, particularly those studying the implications of genetic mutations in populations.

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Homework Statement



I am asked to solve Fisher's equation, i.e. the PDE ut = uxx+u(1-u) .

Then I am asked to describe how the speed of the wave front of solutions to it depend on the amplitude of the initial population with the "mutant gene"

and likewise how does it (the wave front of solutions) depend on the length of the spatial interval occupied by the initial population with the "mutant gene".

I managed to solve the equation and come up with some nice looking plots, but I'm not sure how to analyze them to find the relationships.


Homework Equations





The Attempt at a Solution



I solved the equation, just don't really understand the solutions. Need to find the relationships stated above. I attached a JPEG of my plot.
 

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  • fishplot.jpg
    fishplot.jpg
    45.8 KB · Views: 398
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anyone dealt with the fisher equation?
 

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