Hidden attractors in dynamical systems

Hidden Bifurcations and Attractors in Nonsmooth Dynamical Systems

observational dynamical systems

چکیده در این پایاننامه ابتدا فضاهای متریک فازی را به صورت مشاهدهگرایانه بررسی میکنیم. فضاهای متریک فازی و توپولوژی تولید شده توسط این متریک معرفی شدهاند. سپس بر اساس فضاهایی که در فصل اول معرفی شدهاند آشوب توپولوژیکی، مینیمالیتی و مجموعههای متقاطع در شیوههای مختلف بررسی شده- اند. در فصل سوم مفهوم مجموعههای جاذب فازی به عنوان یک مفهوم پایهای در سیستمهای نیم-دینامیکی نسبی، تعریف شده است. ...

Strange nonchaotic attractors in random dynamical systems.

Whether strange nonchaotic attractors (SNAs) can occur typically in dynamical systems other than quasiperiodically driven systems has long been an open question. Here we show, based on a physical analysis and numerical evidence, that robust SNAs can be induced by small noise in autonomous discrete-time maps and in periodically driven continuous-time systems. These attractors, which are relevant...

On symmetric attractors in reversible dynamical systems

Let ? O(n) be a nite group acting orthogonally on IR n. We say that ? is a reversing symmetry group of a homeomorphism, diieomorphism or ow f t : IR n 7 ! IR n (t 2 Z Z or t 2 IR) if ? has an index two subgroup ~ ? whose elements commute with f t and for all elements 2 ? ? ~ ? and all t , f t (x) = f ?t (x). We give necessary group and representation theoretic conditions for subgroups of revers...

Hidden oscillations in dynamical systems

The classical attractors of Lorenz, Rossler, Chua, Chen, and other widely-known attractors are those excited from unstable equilibria. From computational point of view this allows one to use numerical method, in which after transient process a trajectory, started from a point of unstable manifold in the neighborhood of equilibrium, reaches an attractor and identifies it. However there are attra...