Hölder continuity of three types of generalized synchronization manifolds of non-autonomous systems
The paper considers the following non-autonomous unidirectionally coupled systems \[ \frac{dy}{dt}=g(t,y), \quad \frac{dx}{dt}=Ax +f(t,x) + K (y-x), \] where \(x,y\in\mathbb{R}^n\), \(f(t,y)\) and \(f(t,x)\) are smooth functions, and \(A\), \(K\) are \(n\times n\) constant matrices. For the cases, when the modified response system \[ \frac{dx}{dt}=Ax +f(t,x) - K x \] has an asymptotically stable equilibrium, periodic, or quasiperiodic attractor, sufficient conditions for the existence of Hölder continuous invariant manifold \(S=\{ (t,x,y): x=\Phi(t,y) \}\) are given. The manifold \(S\) is called the generalized synchronization manifold.
scientific article; zbMATH DE number 5649935
scientific article