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Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition
book

Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition

by Harold Klee, Randal Allen
April 2016
Intermediate to advanced content levelIntermediate to advanced
815 pages
31h 29m
English
CRC Press
Content preview from Simulation of Dynamic Systems with MATLAB and Simulink, 2nd Edition
7.3 A three-species predator prey model (Edelstein-Keshet 1988) is
dx
dt
¼ axz þ bxy yx
dy
dt
¼ dy exy
dz
dt
¼ mz(n z) lxy
where
x is a predator
y and z are its prey
(a) Express the nontrivial equilibrium pt (x
e
, y
e
, z
e
) in terms of the system parameters.
(b) Use the ‘‘trim’’ function to nd the equilibrium pt when the system parameters are
a ¼0.075, b ¼0.009, g ¼0.2, d ¼0.1, e ¼0.025, m ¼0.0015, n ¼10, and l ¼0.003.
Compare the answer with the value obtained using the result in part (a).
(c) The equilibrium point is asymptotically stable. Verify by simulating the response of the
autonomous system starting from various randomly selected points in
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Publisher Resources

ISBN: 9781439836736