Page 108

177

CHAPTER 2

38.

Linearity and Nonlinearity

SECTION 2.5

Nonlinear Models: Logistic Equation

y′ = y 2 + y + k

(a)

Setting y′ = 0 yields two equilibria, ye = for k <

(b)

−1 ± 1 −4k , 2

1 1 1 ; none for k > ; one for k = . 4 4 4

The following phase-plane graphs illustrate the bifurcation. 4

y

k=1

t –4

4 no equilibrium points –4 y 4

k = 1/4

t 4 semistable equilibrium

–4

–4 y 4

k = –1

unstable equilibrium t –4

4 stable equilibrium –4

177

Solutions manual for differential equations and linear algebra 2nd edition by farlow ibsn 9780134689  

Solutions Manual for Differential Equations and Linear Algebra 2nd Edition by Farlow IBSN 9780134689548 Full clear download( no error format...

Solutions manual for differential equations and linear algebra 2nd edition by farlow ibsn 9780134689  

Solutions Manual for Differential Equations and Linear Algebra 2nd Edition by Farlow IBSN 9780134689548 Full clear download( no error format...

Advertisement