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Basic Functionality

The basic defining equations for a dynamical system are entered in the following format:

# The Lorenz system (lorenz.def)
x' = sigma ( y - x ) 
y' = rho x - y - x z
z' = -beta z + x y

INITIAL sigma 10 rho 28 beta 2.6667

We denote the time derivative of a variable by a prime, '. This is followed by an equals sign and then the right hand side. A mapping is input in the same format using the prime to indicate the new point in phase space. Variable and parameter names are alphanumeric strings beginning with an alphabetic character. Any undefined string is understood to be a parameter in the system.

Comments are allowed at the end of any line and must begin with the pound character, #. As seen in the above example, multiplication is understood, when no arithmetic operator is present, but it may be explicitly indicated with an asterisk, *. The INITIAL declaration assigns initial values to the parameters.

The parser understands the following fundamental constants, operators, and special functions:

	constants: PI, pi, E
	operators: +, -, *, /, % (mod), ^
	special functions: sin, cos, tan, asin, acos, atan, sinh, cosh, 
	        tanh, log, ln, exp, abs, sqrt
The special functions all correspond to standard C math library functions.

If you try this example, set the dynamical system type setting to Vector field, and then select the ``Build model'' button on the Parser window in order to create the dynamical system from the text.


next up previous contents
Next: Periodic Variables Up: Defining Dynamical Systems Using Previous: Defining Dynamical Systems Using   Contents
2008-05-14