In this paper we consider smooth di erential 1-forms and smooth nonlinear control-a ne systems with (n 1)-inputs evolving on an ndimensional manifold with boundary. These systems are called hypersurface systems under the additional assumption that the drift vector eld and control vector elds span the tangent space to the manifold. We locally classify all structurally stable di erential 1-forms ...

We construct a map from the suspension G-spectrum ?G?M of smooth compact G-manifold to equivariant A-theory spectrum AG(M), and we show that its fiber is, on fixed points, wedge stable h-cobordism spectra. This is constructed as spectral Mackey functors, which compatible with tom Dieck style splitting formulas points. In order reconcile different definitions functor, present new perspective vie...

For dynamical systems with a non hyperbolic equilibrium, it is possible to significantly simplify the study of stability by means center manifold theory. This theory allows isolate complicated asymptotic behavior system close equilibrium point and obtain meaningful predictions its analyzing reduced order on so-called manifold. Since usually not known, good approximation methods are important as...

A three-neuron network model with mixed delays involving multiple discrete and distributed is considered in this paper. Taking the distribute as bifurcation parameters respectively, we investigate stability of system structure conditions for generation Hopf from perspective distribution root characteristic equation linearized at equilibrium state nonlinear system. The intervals that make stable...