Phase line for x' = kxk>0UnstableequilibriumPhase linex个xI0· k<0StableequilibriumPhaselinex↑xI0
Phase line for x’ = kx • k>0 • k<0 x Phase line 0 x Unstable equilibrium x Phase line 0 x Stable equilibrium
The parameter a in x' = ax. Three types of behaviour30a>025 a > O, exponential growth2015- a = O, constant solution-a<O,exponential decrease4.5a<03.52.5α=0x2.51.50.5
The parameter a in x’ = ax • Three types of behaviour – a > 0, exponential growth – a = 0, constant solution – a < 0, exponential decrease 0 1 2 3 4 5 6 7 8 9 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 t x a=0 0 1 2 3 4 5 6 7 8 9 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 a<0 0 1 2 3 4 5 6 7 8 9 0 5 10 15 20 25 30 35 a>0