An Algorithm for Computing Heteroclinic Orbits and Its Application to Chaos Synthesis in the Generalized Lorenz System
Abstract
An algorithm for computing heteroclinic orbitsof nonlinear systems, which can have several hyperbolicequilibria, is suggested and analyzed both analytically andnumerically. The method is based on a representation of theinvariant manifold of a hyperbolic equilibrium via a certainexponential series expansion. The algorithm for computing theseries coefficients is derived and the uniform convergence of theseries is theoretically proved. The algorithm is then applied tocompute heteroclinic orbits numerically in the generalized Lorenzsystem thereby theoretically justifying the previouslydemonstrated existence of chaotic oscillations in this importantclass of dynamical systems.
