Iterating a Cubic Bistable Equation
by
Mike Martin
This page allows you to investigate the dynamics of a cubic bistable difference equation. The equation is:
β
and
α
are the parameters in the equation;
α
is assumed to be between zero and one.
x
_{1}
is the initial value for the sequence -- the first term. This page will generate graphs associated to this sequence, produce the last
M
terms of a sequence that is
T
terms long, and generate the equilibrium values for the difference equation and their stability type. Note that this difference equation is bistable (two stable equilibriums) for certain parameter values. Enter the value of the parameters below, then press Evaluate.
β
=
α
=
T
=
M
=
x
_{1}
=
The graphs are given by:
Numerical values for the last
M
terms of a sequence that is
T
terms long are given by:
The equilibrium values, along with their stability type, are given below: