Global theory of nonlinear systems-chaos, knots and stability
نویسنده
چکیده
Ever since the fundamental ideas of Poincaré in the qualitative theory of dynamical systems, there has been intense interest into the global behaviour of such systems. Many important ideas and examples have grown out of the basic theory including chaos, knotted trajectories, fractal dimension and equivalence theory. Here we shall give an overview of some of the most important results which are crucial to the understanding of the behaviour of such dynamical systems, including chaos, knots and links, approximation techniques, and stability.
منابع مشابه
Global Finite Time Synchronization of Two Nonlinear Chaotic Gyros Using High Order Sliding Mode Control
In this paper, under the existence of system uncertainties, external disturbances, and input nonlinearity, global finite time synchronization between two identical attractors which belong to a class of second-order chaotic nonlinear gyros are achieved by considering a method of continuous smooth second-order sliding mode control (HOAMSC). It is proved that the proposed controller is robust to m...
متن کاملGlobal Stability for Thermal Convection in a Couple Stress Fluid Saturating a Porous Medium with Temperature-Pressure Dependent Viscosity: Galerkin Method
A global nonlinear stability analysis is performed for a couple-stress fluid layer heated from below saturating a porous medium with temperature-pressure dependent viscosity for different conducting boundary systems. Here, the global nonlinear stability threshold for convection is exactly the same as the linear instability boundary. This optimal result is important because it shows that lineari...
متن کاملHybrid Control to Approach Chaos Synchronization of Uncertain DUFFING Oscillator Systems with External Disturbance
This paper proposes a hybrid control scheme for the synchronization of two chaotic Duffing oscillator system, subject to uncertainties and external disturbances. The novelty of this scheme is that the Linear Quadratic Regulation (LQR) control, Sliding Mode (SM) control and Gaussian Radial basis Function Neural Network (GRBFNN) control are combined to chaos synchronization with respect to extern...
متن کاملGlobal Chaos Synchronization of Identical and Nonidentical Chaotic Systems Using Only Two Nonlinear Controllers
In chaos synchronization, the main goal is to design such controller(s) that synchronizes the states of master and slave system asymptotically globally. This paper studied and investigated the synchronization problem of two identical Chen, and identical Tigan chaotic systems and two non-identical Chen and Tigan chaotic systems using Non-linear active control algorithm. In this study, based on L...
متن کاملIIR System Identification Using Improved Harmony Search Algorithm with Chaos
Due to the fact that the error surface of adaptive infinite impulse response (IIR) systems is generally nonlinear and multimodal, the conventional derivative based techniques fail when used in adaptive identification of such systems. In this case, global optimization techniques are required in order to avoid the local minima. Harmony search (HS), a musical inspired metaheuristic, is a recently ...
متن کامل