Tartalomjegyzék

Nonlinear Dynamical Systems (P-ITEEA-0037)

Lecture notes of the seminar

Media files obtained through the computations

Useful Matlab functions and toolboxes

Built-in Matlab functions:

• ode45
• tiledlayout
• nexttile
• quiver
• contour
• surf
• plot

Important functions of Matlab's Symbolic Math Toolbox (SMT):

• syms a x y z real; syms f(x) g(x,y,z) - Declare (create) multiple scalar symbolic variables or functions
• A = sym('a_%d%d',[3 4]) - Create a single symbolic matrix, vector or scalar variable
• f_sym = x^2+y*z; symvars(f_sym) - List symbolic variables appearing in the object passed as an argument
• subs(f_sym, [x z], [x+y x^2]) - Substitute variables or expression by other variables or expression in a symbolic expression
• f_fh = matlabFunction(f_sym, 'vars', {x [y z]}) - Generate a function handle from a symbolic expression
• in(.., type) - Declare that an variables belongs to a collection (i.e. set) of variables, eg. 'real', 'positive', 'integer', 'rational'
• assume(x > 2 & in(y,'rational')) - See: assumeAlso. Clear every other assumptions on the same variables
• assumAlso(in(x,'integer') & in(y,'positive')) - Introduce more assumptions about the symbolic objects
• assumptions - List existing assumptions.
• partfrac - Partial fractional decomposition of a rational function (useful when producing inverse Laplace transformation of a transfer function). FactorMode: real/complex/full/rational. See also its numerical pair: residue.

Other useful functions of Matlab's Symbolic Math Toolbox (SMT):

• combine(sin(x)+cos(x),'sincos') - May be useful when manipulating trigonometric functions
• charpoly - characteristic polynomial of a matrix