The existence of Šilnikov's orbit in four-dimensional Duffing's systems
A Melnikov-type technique is developed for detecting the existence of homoclinic orbits to a saddle-focus equilibrium, so-called Silnikov orbits, in a special class of coupled oscillators. The theory is illustrated for an example in which a Duffing-type oscillator is strongly coupled with a special two-dimensional system. Numerical simulations are given to demonstrate the theoretical results.
scientific article; zbMATH DE number 2101833