Naren is dating a girl named Felicity. Naren and Felicity both cautiously follow their hearts - if
one has positive feelings towards the other, those positive feelings slowly amplify. However,
Naren puts tremendous weight on Felicity's feelings towards him-if Felicity likes him, he likes
her much more, and if Felicity dislikes him, he likes her less. Felicity, on the other hand, does
not like "clingy" people - if Naren likes her more, she tends to like him a little bit less. She is
also susceptible to playing "hard to get"-if Naren dislikes her, she tends to like him more.
Being an engineer, Naren has modeled these emotional dynamics with the following set of
coupled ordinary differential equations: N(t)=0.1N(t)+1F(t)F(t)=0.5N(t)+0.1F(t), Solve the
system of o.d.e.s by hand using eigenvalues and eigenvectors to determine the fate of "Naricity"
if N(0)=1 and F(0)=0, and plot the solution 1 parameterized by t from t=0 to t=15, i.e., plot F(t)
vs. N(t). Then, in a separate plot, plot each trajectory vs. time, i.e., plot N(t) vs. t and F(t) vs. t
together in their own plot. Remember axis labels and legend. What will become of Naricity? You
may use MATLAB's left division to solve systems of linear equations. Suggestion: You must
show your work, but use MATLAB as your calculator because the numbers are a little annoying..
Naren is dating a girl named Felicity. Naren and Felicity both cautio.pdf
1. Naren is dating a girl named Felicity. Naren and Felicity both cautiously follow their hearts - if
one has positive feelings towards the other, those positive feelings slowly amplify. However,
Naren puts tremendous weight on Felicity's feelings towards him-if Felicity likes him, he likes
her much more, and if Felicity dislikes him, he likes her less. Felicity, on the other hand, does
not like "clingy" people - if Naren likes her more, she tends to like him a little bit less. She is
also susceptible to playing "hard to get"-if Naren dislikes her, she tends to like him more.
Being an engineer, Naren has modeled these emotional dynamics with the following set of
coupled ordinary differential equations: N(t)=0.1N(t)+1F(t)F(t)=0.5N(t)+0.1F(t), Solve the
system of o.d.e.s by hand using eigenvalues and eigenvectors to determine the fate of "Naricity"
if N(0)=1 and F(0)=0, and plot the solution 1 parameterized by t from t=0 to t=15, i.e., plot F(t)
vs. N(t). Then, in a separate plot, plot each trajectory vs. time, i.e., plot N(t) vs. t and F(t) vs. t
together in their own plot. Remember axis labels and legend. What will become of Naricity? You
may use MATLAB's left division to solve systems of linear equations. Suggestion: You must
show your work, but use MATLAB as your calculator because the numbers are a little annoying.
