Problem Lotka Volterra Model – Modelling & Plotting in Python


I urgently need your help. Currently I’m conducting a research in regards of the revenue calculation and the dynamics within revenue calculation for my masters. I thought of revenue/profit margin as of a dynamical system – Lotka Volterra differential equations. I thought of a contribution margin calculation as within this simple formula:

https://www.accountingformanagement.org/wp-content/uploads/2012/07/contribution-margin-ratio-img4.png

In consequence my idea was the following, but I receive an error:
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  • Can anyone help me?
  • Do you think it’s a bad idea to use Lotka Volterra equations for this nonlinear purpose of Sales/Cost/Margin Simulation?
  • How would you model it and why? Am I missing equations or does the simple system already fit the requirements?
  • How do I generate a valid plot out of these results (Phase Portrait etc.)?