Howdy, any help with this here
would be a blessing. Thank ya'll!
Solution: 2. Definition: An equilibrium solution is any
constant (horizontal) function that
is a solution to the differential equation.
Stable:
The equilibrium solution is
stable if all solutions with initial conditions
`near' x = c approach
c as
.
Unstable: The
equilibrium solution is
unstable if all solutions with initial conditions
`near' x= c do n
aotpproach c as
.
Semi-stable: The
equilibrium solution is
semi-stable if initial conditions
on one side of c lead
to solutions x(t) that approach c as
,
while initial conditions
on the other side of
c do not approach c.
Construction of one-dimension dynamical system that has three equilibrium points:
(a) Let
(i) Here equilibrium points are given by
Therefore, and
are
three equilibrium solutions.
(ii) For,
is negative, so x(t) is decreasing.
For,
is negative, so x(t) is decreasing.
For,
is positive, so x(t) is increasing.
Thus x(t) = 5 is stable and x(t)= 8 is semi-stable.
(b) Let
Here x=4 is stable and x=6 and x=9 are semistable
Howdy, any help with this here would be a blessing. Thank ya'll! Construct a one-dimension dynamical systems F(x) so that it has 2 three equilibrium points. Moreover, two of them are semi-stable a...
10. Write a one-page summary of the attached paper? INTRODUCTION Many problems can develop in activated sludge operation that adversely affect effluent quality with origins in the engineering, hydraulic and microbiological components of the process. The real "heart" of the activated sludge system is the development and maintenance of a mixed microbial culture (activated sludge) that treats wastewater and which can be managed. One definition of a wastewater treatment plant operator is a "bug farmer", one who controls the aeration...