How to have a max value for a recurrence equation?

Hi there,

Just wondering what I would do if I wanted to created a max value (say x) in a set of recurrence equations? I have this set of equations to model memory. I want to set a max value so that once either of the variables L, N, or F reaches value x, it creates a fixed point and remains there.

for n = (2:m) 
    L(n) = L(n-1)+alpha*(1/L(n-1))
    F(n) = F(n-1)+beta*L(n-1)
    T(n) = L(n-1)-F(n-1); 

Any thoughts?

Answer 1

[Walter Roberson]

You cannot do that with those kinds of equations, not without putting in a conditional definition.

Equations of that form can be [strictly] constant (e.g., alpha and beta are 0). Or they can grow without bound. Or they can oscillate between values. Or they can approach an asymtope. But they cannot reach a steady state except in the constant case.

[Samuel Lee]

Thank you, Walter.

[Walter Roberson]

I missed the possibility that they can grow without bounds while oscillating between negative and positive.