This applet allows one to experiment with differential equations
including Non-ideal relays and
Preisach nonlinearities. You can specify arbitrary
ordinary differential equations to be integrated using
fourth order Runge-Kutta method. The equations should
be in form  , where  has one up to 9
dimensions. All common mathematical functions (like sin,
sqrt, exp etc.) can be used, as well as hysteresis operators.
There are two types of operators supported: Preisach operator
(which can be inserted as p1(y) to p9(y))
and Relay operator (r1(y) to r9(y)).
Note that each hysteresis operator
can be used only once in the equations.
To plot a solution of differential-operator equations,
use the + and - buttons to add a required number
of equations, then input right-hand sides of each equation.
In one-dimensional case the variable is called x.
In multi-dimensional case, the variables are called x1,
x2 etc. Then specify integration bounds t0
and t1, integration step h, and initial
values xi(t0). Then click the ``Solve'' button.
The ``Export'' button saves plot points in a file which
can be copied into Mathematica to use by the ListPlot function.
The solutions can be plotted either on the  plane
or on  plane. Additionally, inputs and outputs
of hysteresis operators can be plotted on different planes.
The direction of trajectories can be found by spotting
the initial point  on the plot.
The limitation of the applet is that parameters and
initial states of hysteresis operators are fixed. The Preisach
operators are defined by uniform measure on a triangle
bounded by lines  ,  and  , and take values
in range 0 to 1. Initially the state triangle is empty.
The Relay operators have thesholds -1 and 1, the output is
either 0 or 1, and the initial state is 0. In the moment of
time  the states of operators are updated according to
initial value .
Some examples of equations with Preisach nonlinearities are:
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