# Software Listing of Author : "Moiseev Igor"

AGM calculates the Artihmetic Geometric Mean of A and B (see [1]). The function is used in routines ELLIPJ and ELLIPTIC12. [A,B,C,N] = AGM(A0,B0,C0,TOL) carry out the process of the arithmetic geometric mean, starting with a given positive numbers triple (A0,B0,C0) and returns in (A,B,C) the generated sequence. N is a number of steps (returns in the type uint32).

• Platform: Matlab, Scripts

ELLIPTIC12i evaluates the Incomplete Elliptic Integrals of the First, Second Kind and Jacobi's Zeta Function for the complex value of phase U. Parameter M must be in the range 0 <= M <= 1. [Fi,Ei,Zi] = ELLIPTIC12i(U,M,TOL) where U is a complex phase in radians, M is the real parameter and TOL is the tolerance (optional). Default value for the tolerance is eps = 2.220e-16. ELLIPTIC12i uses the function ELLIPTIC12 to evaluate the values of corresponding integrals. See also ELLIPKE, ELLIPJ, ELLIPTIC12.

• Platform: Matlab, Scripts

[Th, H] = JACOBITHETAETA(U,M) returns the values of the Jacobi's theta and eta elliptic functions TH and H evaluated for corresponding elements of argument U and parameter M.

• Platform: Matlab, Scripts

The Lorenz attractor, named for Edward N. Lorenz, is an example of a non-linear dynamic system corresponding to the long-term behavior of the Lorenz oscillator. The Lorenz oscillator is a 3-dimensional dynamical system that exhibits chaotic flow, noted for its lemniscate shape. The map shows how the state of a dynamical system (the three variables of a three-dimensional system) evolves over time in a complex, non-repeating pattern. Wiki Article: http://en.wikipedia.org/wiki/Lorenz_attractor % LORENZ Function generates the lorenz attractor of the prescribed values % of parameters rho, sigma, beta % % [X,Y,Z] = LORENZ(RHO,SIGMA,BETA,INITV,T,EPS) % X, Y, Z - output vectors of the strange attactor trajectories % RHO - Rayleigh number % SIGMA - Prandtl number % BETA - parameter % INITV - initial point % T - time interval % EPS - ode...

• Platform: Matlab, Scripts
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