On a cross coupling of Rulkov neural maps

What the math gives to ML

The paper provides a constructive boundedness mechanism for discrete fast-slow systems: if the linear component has all eigenvalues strictly inside the unit disk and the nonlinear forcing is uniformly bounded, an absorbing set exists. Its cross-coupling construction additionally preserves a snap-back repeller, and therefore a certified chaotic invariant set, under suitable local inverse and nondegeneracy conditions. The strongest neural-network transfer is a bounded cross-coupled recurrent or reservoir architecture whose slow memory is spectrally contractive while its fast nonlinear subdynamics remain expressive. Jacobian and state-radius diagnostics can test whether coupling creates a useful high-dimensional attractor rather than uncontrolled exploding dynamics.