A Geometric Model for Pseudohyperbolic Shilnikov Attractors

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.