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Consider a theoretical model for mutual inhibition in ecological systems where n > 0 measures the strength of mutual inhibition d = x(t) = dt (1/2)" (1/2)" +yn X d dt³ (t) = (1/2)" (1/2)" +x" y Plot the nullclines and determine the equilibria points for n = 1 and n = 3. Interpret these equilibrium in the ecological setting. Explicitly calculate the local stability of the equilibrium point where x* = y* for gen- eral n. When does the system undergo a qualitative change in behaviour?

Consider a theoretical model for mutual inhibition in ecological systems where n > 0 measures the strength of mutual inhibition d = x(t) = dt (1/2)" (1/2)" +yn X d dt³ (t) = (1/2)" (1/2)" +x" y Plot the nullclines and determine the equilibria points for n = 1 and n = 3. Interpret these equilibrium in the ecological setting. Explicitly calculate the local stability of the equilibrium point where x* = y* for gen- eral n. When does the system undergo a qualitative change in behaviour?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider a theoretical model for mutual inhibition in ecological systems where n > 0 measures the strength of mutual inhibition d dt x(t) = (1/2)" (1/2)" +yn - x d dt (t) = (1/2)" - (1/2)" +x" -y Plot the nullclines and determine the equilibria points for n = 1 and n = 3. Interpret these equilibrium in the ecological setting. Explicitly calculate the local stability of the equilibrium point where x* = y* for gen- eral n. When does the system undergo a qualitative change in behaviour?
Transcribed Image Text:Consider a theoretical model for mutual inhibition in ecological systems where n > 0 measures the strength of mutual inhibition d dt x(t) = (1/2)" (1/2)" +yn - x d dt (t) = (1/2)" - (1/2)" +x" -y Plot the nullclines and determine the equilibria points for n = 1 and n = 3. Interpret these equilibrium in the ecological setting. Explicitly calculate the local stability of the equilibrium point where x* = y* for gen- eral n. When does the system undergo a qualitative change in behaviour?
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