A Geometric Model for Pseudohyperbolic Shilnikov Attractors

Abstract We describe a $$C^{1}$$ -open set of systems of differential equations in $$R^{n}$$ , for any $$n\geqslant 4$$ , where every system has a chain-transitive chaotic attractor which contains a saddle-focus equilibrium with a two-dimensional unstable manifold. The attractor also includes a wild hyperbolic set and a heterodimensional cycle involving hyperbolic sets with different numbers of positive Lyapunov exponents.