In this paper, a fuzzy controller is designed for stabilization of the Lorenz chaotic equations. A simple Mamdani inference method is used for this purpose. This method is very simple and applicable for complex chaotic systems and it can be implemented easily. The stability of close loop system is investigated by the Lyapunov stabilization criterion. A Lyapunov function is introduced and the gl...

The discussion on the relation between the Kolmogorov system, considered as low-order approximation of Navier–Stokes equations, and the well-known Lorenz equations is still not completely understood. In this Letter, referring to the mathematical theory of motion on Lie groups, a particular class of Kolmogorov systems, largely studied in low-dimensional models of geophysical fluid dynamics, is e...

We address the issue of multi-parameter estimation from scalar outputs of chaotic systems, using the dynamics of a Malkus water wheel and simulations of the corresponding Lorenz-equations model as an example. We discuss and compare two estimators: one is based on a globally convergent adaptive observer and the second is an extended Kalman filter (EKF). Both estimators can identify all three unk...

One of the most important phenomenons in some systems is chaos; so control chaotic systems is difficult and shows the abilities of control methods. In this paper, first known chaotic systems, Lorenz equations, was selected as a chaotic system. One of the best control methods that would be used for stabilization this system, was Backstepping. In this paper this method is improved to Generalized ...

In this paper, we develop, analyze, and evaluate a parallel algorithm for diagonally explicit Runge Kutta method of order four (DERK4) for solving systems of differential equations. A timing model has been developed and verified to estimate the execution time of the proposed algorithm. We used the proposed algorithm to solve a predatorprey system and Lorenz equation numerically. The numerical r...

Abstract We investigate the parametric evolution of riddled basins related to synchronization of chaos in two coupled piecewise-linear Lorenz maps. Riddling means that the basin of the synchronized attractor is shown to be riddled with holes belonging to the basin of infinity in an arbitrarily fine scale, what has serious consequences on the predictability of the final state for such a coupled ...

We prove that a singular-hyperbolic (or Lorenz-like) attractor of a 3-dimensional flow is chaotic, in two strong different senses. Firstly, the flow is expansive: if two points remain close for all times, possibly with time reparametrization, then their orbits coincide. Secondly, there exists a physical (or Sinai-Ruelle-Bowen) measure supported on the attractor whose ergodic basin covers a full...

A remarkably simple electronic circuit design based on the chaotic Lorenz system is described. The circuit consists of just two active nonlinear elements (high-speed analog multipliers) and a few passive linear elements. Experimental implementations of the circuit exhibit the classic butterfly attractor and the hysteretic transition from steady state to chaos observed in the Lorenz equations. T...

Diffusionless Lorenz equations (DLE) are a simple one-parameter version of the wellknown Lorenz model, which was obtained in the limit of high Rayleigh and Prandtl numbers, physically corresponding to diffusionless convection. A simple control method is presented to control chaos by using periodic parameter perturbation in DLE. By using the generalized Melnikov method, the parameter conditions ...

In classical data assimilation using sequential Monte Carlo methods, a physical model is run at each time steps to simulate members corresponding to different forecast scenarios. In this paper, we propose to use statistical analogs provided by observational or model-simulated data to emulate the dynamical model and generate relevant forecast members. This new methodology is called AnEnKF/AnEnFS...