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Calculate the equilibria of the dynamical system.
Equilibria:
If there is more than one equilibrium, enter them in increasing order, separated by commas. (The number $W$ is positive.)
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If $a = 0.9$, determine the stability of the equilibria.
Specify the stability of each equilibrium in the same order as above. Enter stable if an equilibrium is stable or unstable if it is unstable. Separate answers by commas.
Equilibria are stable:
For example, if there are four equilibria and they are, in order, stable, unstable, unstable, and unstable, then you should enter stable, unstable, unstable, unstable in the answer blank.
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If $a = 0.9$, $W = 490$, and the initial population is $c_0=770$, what will happen to the population after a long time?
After a long time, the population size will approach
cheetahs.
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If $a = 3.3$, determine the stability of the equilibria.
Specify the stability of each equilibrium in the same order as above. Enter stable if an equilibrium is stable or unstable if it is unstable. Separate answers by commas.
Equilibria are stable:
For example, if there are four equilibria and they are, in order, stable, unstable, unstable, and unstable, then you should enter stable, unstable, unstable, unstable in the answer blank.
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For what range of $a$ is there a stable nonzero equilibrium?
There is a stable nonzero equilibrium for
$< a < $
.