A model system is proposed, which manifests a blue sky catastrophe giving rise to a hyperbolic attractor of Smale–Williams type in accordance with theory of Shilnikov and Turaev. Some essential features of the transition are demonstrated in computations, including Bernoulli-type discrete-step evolution of the angular variable, inverse square root dependence of the first return time on the bifurcation parameter, certain type of dependence of Lyapunov exponents on control parameter for the differential equations and for the Poincaré map.
Keywords:
attractor, bifurcation, Smale–Williams solenoid, Lyapunov exponent
Citation:
Kuznetsov S. P., Example of blue sky catastrophe accompanied by a birth of Smale–Williams attractor, Regular and Chaotic Dynamics,
2010, Volume 15, Numbers 2-3,
pp. 348-353