A rigorous solution of the chaotic Lozi mapping

نویسندگان

  • Zeraoulia Elhadj
  • J. C. Sprott
چکیده

In this letter, a rigorous solution of the chaotic Lozi mapping is given for some regions of the bifurcation parameters. The relevance of this result is that while chaos has been proved for the Lozi mapping, there has not previously been discussion of the possibility of finding a rigorous formula for this solution. This important result is obtained using the Jordan normal form defined for matrices.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Robust Coordinated Design of UPFC Damping Controller and PSS Using Chaotic Optimization Algorithm

A Chaotic Optimization Algorithm (COA) based approach for the robust coordinated design of the UPFC power oscillation damping controller and the conventional power system stabilizer has been investigated in this paper. Chaotic Optimization Algorithms, which have the features of easy implementation, short execution time and robust mechanisms of escaping from local optimum, is a promising tool fo...

متن کامل

A unified piecewise smooth chaotic mapping that contains the Hénon and the Lozi systems

In this paper we introduce a new piecewise smooth mapping of the plane as a unified discrete-time chaotic system that contains the original H ́enon and Lozi systems as two extremes and other systems as a transition in between and that has robust homoclinic chaos over a portion of its key system parameters. Dynamical behaviors of the unified system are investigated in some detail.

متن کامل

Tuning of PID controller for an automatic regulator voltage system using chaotic optimization approach

Despite the popularity, the tuning aspect of proportional–integral-derivative (PID) controllers is a challenge for researchers and plant operators. Various controllers tuning methodologies have been proposed in the literature such as auto-tuning, self-tuning, pattern recognition, artificial intelligence, and optimization methods. Chaotic optimization algorithms as an emergent method of global o...

متن کامل

A New Chaotic Attractor from 2d Discrete Mapping via Border-collision Period-doubling Scenario

The discreet mathematical models are gotten directly via scientific experiences, or by the use of the Poincaré section for the study of a continuous model. One of these models is the Henon map. Many papers have described chaotic systems, one of the most famous being a two-dimensional discrete map which models the original Henon map [3, 4, 5, 7, 8]. Moreover, it is possible to change the form of...

متن کامل

The Chaotic Saddle in the Lozi Map, Autonomous and Nonautonomous Versions

In this paper, we prove the existence of a chaotic saddle for a piecewise-linear map of the plane, referred to as the Lozi map. We study the Lozi map in its orientation and area preserving version. First, we consider the autonomous version of the Lozi map to which we apply the Conley–Moser conditions to obtain the proof of a chaotic saddle. Then we generalize the Lozi map on a nonautonomous ver...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013