OA R-1 R (S,)=A+A(S,) + R+1(1+R)2a /(S,z)=I+/(S,) 2Q(1+R)A-Q/+P A'(S,)=A(T)cos() trial solution I(s, t=I(o)cos(
2 2 2 2 2 ' 2 (1 ) ' ' ' ' ' (1 ) ' 1 ' 1 s I Q R A QI P I s A I R R A R A R ∂ ∂ = + − + ∂ ∂ ∂ ∂ + + − + − = ∂ ∂ τ τ ( , ) '( , ) ( , ) '( , ) τ τ τ τ I s I I s A s A A s = + = + ( ) cos( ) ˆ '( , ) ( ) cos( ) ˆ '( , ) l l s I s I s A s A τ τ τ τ = = trial solution: 6
A'(s,D=A(Tcos( A I'(s, t)=l(T)cos( (S,τ (S,)=A+A(S,) (S,)=1+/(S,t)
7 ( ) cos( ) ˆ '( , ) ( ) cos( ) ˆ '( , ) l l s I s I s A s A τ τ τ τ = = A I s s A I I’(s,τ) ( , ) '( , ) ( , ) '( , ) τ τ τ τ I s I I s A s A A s = + = +
dA(R-11 R s. T TCOS dr\R+12)(1+R) "(S,z)=()cos( d P =2Q(1+R)A-Q+ dt R-11 P 2OR stability 0+ R+12人c2)1+R inhomogeneous P(R-1 solution Q R+1 Q、R-1 P R+l
I P Q R A Q ddI I R R A R R d dA ˆ ˆ 2 (1 ) ˆ ˆ (1 ) ˆ 1 1 1 ˆ 2 2 2 ⎟⎠⎞ ⎜⎝⎛ = + − + + ⎟ − ⎠⎞ ⎜⎝⎛ − +− = l l τ τ ( ) cos( ) ˆ '( , ) ( ) cos( ) ˆ '( , ) l l s I s I s A s A τ τ τ τ = = 0 1 1 1 0 1 1 2 1 1 2 2 2 2 ⎟ <⎠⎞ ⎜⎝⎛ − +− + − > + ⎟ +⎠⎞ ⎜⎝⎛⎟ + ⎠⎞ ⎜⎝⎛ − +− − l l l l R P R Q R P QR Q RR stability inhomogeneous solution 1 1 + − > R R P Q 8
R-1 homogeneous stability R+1 stability against spatial distrubance: ,R-I P R+l (S,τ if P <1 D<Da), systems is always stable, against any perturbation both spatial and temporal
1 1 + − > R R Q homogeneous stability: stability against spatial distrubance: 1 1 + − > R R P Q s I I’(s,τ) I 9 if P < 1 (Di<Da), systems is always stable, against any perturbation both spatial and temporal
homogeneously stable I relaxes back to previous value after small uniform disturbance △A△△ I' relaxes back to stable against spatial disturbance after small spatial disturbance
s I I homogeneously stable: I relaxes back to previous value after small uniform disturbance s I I I’ relaxes back to after small spatial disturbance I stable against spatial disturbance: 10