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Computation of periodic orbits of non-autonomous systems and fixed points of maps using Newton method

C 100.00%
fixed-points stroboscopic-map newton-method

po_periodic_systems's Introduction

Computation of periodic orbits for non-autonomous systems

These routines compute the initial conditions for a periodic orbit of a non-autonomous with periodic dependence on time:

$\displaystyle \dot{x}=f(x,t),\quad f(x,t+T)=f(x,t).$    

That is, the goal is to compute a point $ x^*$ such that, for a given $ t_0$,

$\displaystyle \varphi(t_0+qT;x)=x.$    

The method used consists on performing a Newton method to solve the equation

$\displaystyle S_{t_0}(x)-x=0,$    

where $ S_{t_0}$ is the stroboscopic map (time $ qT$ return map):

$\displaystyle S_{t_0}(x)=\varphi(t_0+qT;x)$    

The program needs the gsl libraries, and can be compiled using
g++ -o main main.c rk78.c lu.c memory.c -lgsl -lgslcblas

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