AN ALGORITHM FOR COMPUTING HETEROCLINIC ORBITS AND ITS APPLICATION TO CHAOS SYNTHESIS IN THE GENERALIZED LORENZ SYSTEM

In this paper, an algorithm for computing heteroclinic orbits of nonlinear systems, which can have several hyperbolic equilibria, is suggested and analyzed both analytically and numerically. The method is based on a representation of the invariant manifold of a hyperbolic equilibrium via a certain exponential series expansion. The algorithm for computing the series coefficients is derived and the uniform convergence of the series is theoretically proved. The algorithm is then applied to computing heteroclinic orbits numerically in the generalized Lorenz system, thereby theoretically justifying the previously demonstrated existence of chaotic oscillations in this important class of dynamical systems.