Patterns
From
Reaction-
Diffusion Systems
Philosophical Transactions of the Royal Society of London. Series B,
Biological Sciences, Vol. 237, No. 641. (Aug. 14, 1952), pp. 37-
72
Stable uniform state in a reaction syste
Summary for Stability for Reaction-Diusion Problems
One Equation
c
2c
= D 2 + f (c)
t
x
Uniform Steady-state : f () = 0
c
Stability : A steady-state is asymptotically stable if f (c) < 0 and it is unstable if f (c) > 0
Two Equations
u
2u
= D1 2 + f (u,
Summary for Nonlinear IVPs
Single Equations
y = f (y )
Steady-state : f () = 0
y
Stability : The steady-state is asymptotically stable if f (y ) < 0 and it is unstable if f (y ) > 0.
Systems of Two Equations
x = f (x, y )
y = g (x, y )
Steady-state : f (,
Summary for Nonlinear Dierence Equations
Single Equations
xn+1 = f (xn )
Steady-state : x = f ()
x
Stability : The steady-state is asymptotically stable if |f (x)| < 1 and it is unstable if
|f (x)| > 1.
Systems of Two Equations
xn+1 = f (xn , yn )
yn+1 =