12. [Kaplan & Glass(1995)] Limpets and seaweed live in a tide pool. The dynamics of this system are given by the differential equations ds s – s² – sl, dt dl = sl dt 1², 1>0,s>0, 2 where the densities of seaweed and limpets are given by s and l, respectively. (i) Determine all equilibria of this system. (ii) For each nonzero equilibrium determined in part (a), evaluate the stability and classify it as a node, focus, or saddle point. (iii) Sketch the flows in the phase plane.
12. [Kaplan & Glass(1995)] Limpets and seaweed live in a tide pool. The dynamics of this system are given by the differential equations ds s – s² – sl, dt dl = sl dt 1², 1>0,s>0, 2 where the densities of seaweed and limpets are given by s and l, respectively. (i) Determine all equilibria of this system. (ii) For each nonzero equilibrium determined in part (a), evaluate the stability and classify it as a node, focus, or saddle point. (iii) Sketch the flows in the phase plane.
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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